The Eye-Conic Multi-Finish Palettes launch this July and come in six different color schemes.
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Image quality is grainy but last time we saw the NRV (bi-conic) nose cone was on a ER-Scud. pic.twitter.
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Gaultier is best known for some of his sexy designs and stage costumes, including a conic bra worn by singer Madonna.
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"A common insecurity is when men come to us and have this conic breast tissue—that opens the door to pec implants," he explained.
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And by 1950, the brand debuted the V-Conic, marketed as the first mass-produced, high quality watch movement made in the United States.
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Close-ups of the film's "star" pan across leaking conic growths, patches of rough hair (human hair?), and hills and valleys of uneven, alien skin.
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" Mori created the warm eye look using the Marc Jacobs Beauty Eye-Conic Multi-Finish Eyeshadow Palette, which she says helped "balance the softness of her fresh skin.
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He has long embraced the world of show business, and most famously dressed singer Madonna in a conic bra and bustier on her "Blonde Ambition" tour in 1990.
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I added a little bit of the black color in the Marc Jacobs Beauty Eye-Conic Steel(etto) Palette to make it look even smokier and grittier, and that was it.
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The new Eye-Conic Multi-Finish Eyeshadow Palettes ring in at $49 and are tucked into the same seven-pan packaging that fits sleekly in your makeup bag — but that's where the similarities end.
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Now, I am obviously no mathematically whiz (evident by the fact that I spend my free time viewing my math teacher's YouTube channel), but surely there is nothing too scandalous about conic sections, complex dynamics, and correlation values.
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It follows dually that a line conic has two of its lines through every point and any envelope of lines with this property is a line conic. At every point of a point conic there is a unique tangent line, and dually, on every line of a line conic there is a unique point called a point of contact. An important theorem states that the tangent lines of a point conic form a line conic, and dually, the points of contact of a line conic form a point conic..
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Conic TV, Conic Film Productions, Contec Sound Media, Conic Video Club, Grand Precision Works, Soundic Electronics, as well as Conic Semiconductor, etc. were remained private. In 1983, Conic Investment purchased Conic Investment Building from the developer Cheung Kong Holdings, by paying HK$53.3 million cash and issuing new shares worth HK$56.7 million (HK$2.1 per share) to Cheung Kong, that equal to 7.2% of the original share capital according to news report. The building became the headquarter of Conic Investment.
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1\. Definition of the Steiner generation of a conic section The Steiner conic or more precisely Steiner's generation of a conic, named after the Swiss mathematician Jakob Steiner, is an alternative method to define a non- degenerate projective conic section in a projective plane over a field. The usual definition of a conic uses a quadratic form (see Quadric (projective geometry)). Another alternative definition of a conic uses a hyperbolic polarity. It is due to K. G. C. von Staudt and sometimes called a von Staudt conic.
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In geometry, an eleven-point conic is a conic associated to four points and a line, containing 11 special points.
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Since P is across side AC, the 9-point conic is a nine-point hyperbola in this instance. When P is inside triangle ABC the 9-point conic is a nine-point circle. In geometry, the nine-point conic of a complete quadrangle is a conic that passes through the three diagonal points and the six midpoints of sides of the complete quadrangle. The nine-point conic was described by Maxime Bôcher in 1892.
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So the cubic has a component in common with the conic which must be the conic itself, so is the union of the conic and a line. It is now easy to check that this line is the Pascal line.
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The larger Conic Group also had a TV studio called Conic TV Studio, which was now known as Centro TV (), a predecessor of Centro Digital Pictures. Conic TV was led by Robert Chua and John Chu (); Chu later bought the company from [the larger] Conic Group. A sister company, Conic Video Club, was opened in 1982. In 1980, Conic Investment was already one of the largest electronic manufacturer in Hong Kong. In November 1980, Conic Investment signed a land lease with a government-owned corporation, Hong Kong Industrial Estates Corporation, in order to open a CRT television factory in the Tai Po Industrial Estate. Conic Investment also invested in the mainland China shortly after the marketisation, which a Sino-foreign joint venture repairing factory in Fuzhou, for Conic and Contec branded products, was opened in April 1980. It became a listed company on the Hong Kong stock exchange on 25 August 1981. The listed company received half of the former Conic Group, while some of the former subsidiaries remained private, under another holding company Honic Holdings (), which was incorporated on 18 December 1979.
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It is also possible to describe all conic sections in terms of a single focus and a single directrix, which is a given line not containing the focus. A conic is defined as the locus of points for each of which the distance to the focus divided by the distance to the directrix is a fixed positive constant, called the eccentricity e. If e is between zero and one the conic is an ellipse; if e=1 the conic is a parabola; and if e>1 the conic is a hyperbola. If the distance to the focus is fixed and the directrix is a line at infinity, so the eccentricity is zero, then the conic is a circle.
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Bôcher notes that when P is the orthocenter, one obtains the nine-point circle, and when P is on the circumcircle of ABC, then the conic is an equilateral hyperbola. In 1912 Maud Minthorn showed that the nine- point conic is the locus of the center of a conic through four given points.
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Conic Investment also owned the brand Contec (). [the larger] Conic Group also had a film production company, Conic Film Productions Limited () that was incorporated in October 1979. signed a contract to publish the album of Sam Hui in 1984. The audio department of the [larger] Conic Group, which publish albums for aforementioned Sam Hui, as well as Michael Kwan and Paula Tsui, was operated by Contec Sound Media Limited (, incorporated in April 1981) according to other news report.
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Apollonius of Perga made significant advances in the study of conic sections. Apollonius of Perga (c. 262–190 BC) made significant advances to the study of conic sections, showing that one can obtain all three varieties of conic section by varying the angle of the plane that cuts a double-napped cone. He also coined the terminology in use today for conic sections, namely parabola ("place beside" or "comparison"), "ellipse" ("deficiency"), and "hyperbola" ("a throw beyond").
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In the corresponding affine space, one obtains an ellipse if the conic does not intersect the line at infinity, a parabola if the conic intersects the line at infinity in one double point corresponding to the axis, and a hyperbola if the conic intersects the line at infinity in two points corresponding to the asymptotes.
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The size of the shell varies between 20 mm and 40 mm. The solid, imperforate shell has a conic shape. Its color pattern is brown or gray. The conic spire is acute.
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In a projective space over any division ring, but in particular over either the real or complex numbers, all non-degenerate conics are equivalent, and thus in projective geometry one simply speaks of "a conic" without specifying a type. That is, there is a projective transformation that will map any non-degenerate conic to any other non- degenerate conic. The three types of conic sections will reappear in the affine plane obtained by choosing a line of the projective space to be the line at infinity. The three types are then determined by how this line at infinity intersects the conic in the projective space.
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Conic LC molecules, like in discotics, can form columnar phases. Other phases, such as nonpolar nematic, polar nematic, stringbean, donut and onion phases, have been predicted. Conic phases, except nonpolar nematic, are polar phases.
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The world on an equidistant conic projection. 15° graticule, standard parallels of 20°N and 60°N. The equidistant conic projection with Tissot's indicatrix of deformation. Standard parallels of 15°N and 45°N.
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This definition can be generalized further: one may speak of points in general position with respect to a fixed class of algebraic relations (e.g. conic sections). In algebraic geometry this kind of condition is frequently encountered, in that points should impose independent conditions on curves passing through them. For example, five points determine a conic, but in general six points do not lie on a conic, so being in general position with respect to conics requires that no six points lie on a conic.
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Lambert conformal conic projection with standard parallels at 20°N and 50°N. Projection extends toward infinity southward and so has been cut off at 30°S. The Lambert conformal conic projection with standard parallels at 15°N and 45°N, with Tissot's indicatrix of deformation. Aeronautical chart on Lambert conformal conic projection with standard parallels at 33°N and 45°N°.
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The sinistral or dextral shell is imperforate, conic-oblong and solid. The shell has 6 whorls. The spire is slightly convexly-conic and the apex subacute. The suture is margined and the whorls are slightly convex.
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A general conic is defined by five points: given five points in general position, there is a unique conic passing through them. If three of these points lie on a line, then the conic is reducible, and may or may not be unique. If no four points are collinear, then five points define a unique conic (degenerate if three points are collinear, but the other two points determine the unique other line). If four points are collinear, however, then there is not a unique conic passing through them – one line passing through the four points, and the remaining line passes through the other point, but the angle is undefined, leaving 1 parameter free.
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The paraboloid shape of Archeocyathids produces conic sections on rock faces Conic sections are important in astronomy: the orbits of two massive objects that interact according to Newton's law of universal gravitation are conic sections if their common center of mass is considered to be at rest. If they are bound together, they will both trace out ellipses; if they are moving apart, they will both follow parabolas or hyperbolas. See two-body problem. The reflective properties of the conic sections are used in the design of searchlights, radio-telescopes and some optical telescopes.
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Diagonal triangle of quadrangle on conic. Polars of diagonal points are colored the same as the points. The theory of poles and polars of a conic in a projective plane can be developed without the use of coordinates and other metric concepts. Let be a conic in where is a field not of characteristic two, and let be a point of this plane not on .
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By the Principle of Duality in a projective plane, the dual of each point is a line, and the dual of a locus of points (a set of points satisfying some condition) is called an envelope of lines. Using Steiner's definition of a conic (this locus of points will now be referred to as a point conic) as the meet of corresponding rays of two related pencils, it is easy to dualize and obtain the corresponding envelope consisting of the joins of corresponding points of two related ranges (points on a line) on different bases (the lines the points are on). Such an envelope is called a line conic (or dual conic). In the real projective plane, a point conic has the property that every line meets it in two points (which may coincide, or may be complex) and any set of points with this property is a point conic.
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The size of the shell varies between 5 mm and 21 mm. The solid, umbilicate shell has a globose-conic shape. Its color is black, brown, or grayish-pink, either unicolored or tessellated with dark spots. The conic spire is short.
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Ovately conic. Shaped like an egg, but with a somewhat conic apex, as some gastropods. Oviparous. Bringing forth young in an egg which is hatched after it is laid. Ovisac. A pouch in which the eggs or embryos are contained. Ovoviviparous.
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The directrix of a conic section can be found using Dandelin's construction. Each Dandelin sphere intersects the cone at a circle; let both of these circles define their own planes. The intersections of these two parallel planes with the conic section's plane will be two parallel lines; these lines are the directrices of the conic section. However, a parabola has only one Dandelin sphere, and thus has only one directrix.
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A conic section can be created using five points near the end of the known data. If the conic section created is an ellipse or circle, when extrapolated it will loop back and rejoin itself. An extrapolated parabola or hyperbola will not rejoin itself, but may curve back relative to the X-axis. This type of extrapolation could be done with a conic sections template (on paper) or with a computer.
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Nicoteles of Cyrene () (c. 250 BCE) was a Greek mathematician from Cyrene. He is mentioned in the preface to Book IV of the Conics of Apollonius, as criticising Conon concerning the maximum number of points with which a conic section can meet another conic section. Apollonius states that Nicoteles claimed that the case in which a conic section meets opposite sections could be solved, but had not demonstrated how.
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Conic Hill (from Gaelic "coinneach" meaning moss) is a prominent hill in Stirling, Scotland.
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In particular Apollonius of Perga's famous Conics deals with conic sections, among other topics.
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If seven of the points lie on a conic, then the ninth point can be chosen on that conic, since will always contain the whole conic on account of Bézout's theorem. In other cases, we have the following. :If no seven points out of are co-conic, then the vector space of cubic homogeneous polynomials that vanish on (the affine cones of) (with multiplicity for double points) has dimension two. In that case, every cubic through also passes through the intersection of any two different cubics through , which has at least nine points (over the algebraic closure) on account of Bézout's theorem.
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The size of the shell varies between 35 mm and 50 mm. The imperforate, solid shell has an ovate-conic shape. Its color pattern is whitish, streaked and maculated with brown or green, the darker color often predominating. The conic spire is acute.
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The size of the shell varies between 4 mm and 8 mm. The small, solid and thick shell has a globose conic shape. It is pinkish, or ashen-pink, irregularly dotted or longitudinally striped with dull red. The short spire is acutely conic.
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The proof makes use of the property that for every conic section we can find a one-sheet hyperboloid which passes through the conic. There also exists a simple proof for Pascal's theorem for a circle using the law of sines and similarity.
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An illustration of various conic constants In geometry, the conic constant (or Schwarzschild constant, after Karl Schwarzschild) is a quantity describing conic sections, and is represented by the letter K. The constant is given by :K = -e^2, where e is the eccentricity of the conic section. The equation for a conic section with apex at the origin and tangent to the y axis is :y^2-2Rx+(K+1)x^2=0 where R is the radius of curvature at x = 0\. This formulation is used in geometric optics to specify oblate elliptical (K > 0), spherical (K = 0), prolate elliptical (0 > K > −1), parabolic (K = −1), and hyperbolic (K < −1) lens and mirror surfaces. When the paraxial approximation is valid, the optical surface can be treated as a spherical surface with the same radius.
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Suppose is the cubic polynomial vanishing on the three lines through and is the cubic vanishing on the other three lines . Pick a generic point on the conic and choose so that the cubic vanishes on . Then is a cubic that has 7 points in common with the conic. But by Bézout's theorem a cubic and a conic have at most 3 × 2 = 6 points in common, unless they have a common component.
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The association of lines of the pencils can be extended to obtain other points on the ellipse. The constructions for hyperbolas and parabolas are similar. Yet another general method uses the polarity property to construct the tangent envelope of a conic (a line conic).
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The length of the shell varies between 20 mm and 54 mm. The imperforate shell has an ovate-conic shape. Its color pattern is brown, olive or gray, above radiately marked, below irregularly maculated with snowy white, sometimes dark, unicolored. The conic spire is acute.
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Certain special cases of conic optimization problems have notable closed-form expressions of their dual problems.
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This is an abundant species that is variable both in color and the prominence of the sculpture. The solid, imperforate shell has an ovate-conic shape. It is orange-colored, brown or gray, sometimes banded, flammulated, or maculated with white or brown. The conic spire is acute.
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The height of the shell varies between 10 mm and 14 mm, its diameter between 12 mm and 19 mm. The small, solid, imperforate shell has a depressed-conic shape. Its color pattern is golden yellow or olive. The spire is low-conic and contains five whorls.
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Type species of the subgenus Bulimella is Achatinella byronii Newcomb. Subgenus Achatinellastrum Pfeiffer, 1854: The shell is imperforate, ovate-conic or oblong-conic and smooth. The embryonic whorls are not flattened. The outer lip is thin or only slightly thickened within the apex but not expanded.
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In the Cartesian coordinate system, the graph of a quadratic equation in two variables is always a conic section (though it may be degeneratethe empty set is included as a degenerate conic since it may arise as a solution of this equation), and all conic sections arise in this way. The most general equation is of the form :Ax^2 + Bxy + Cy^2 +Dx + Ey + F = 0, with all coefficients real numbers and not all zero.
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In projective geometry, a von Staudt conic is the point set defined by all the absolute points of a polarity that has absolute points. In the real projective plane a von Staudt conic is a conic section in the usual sense. In more general projective planes this is not always the case. Karl Georg Christian von Staudt introduced this definition in Geometrie der Lage (1847) as part of his attempt to remove all metrical concepts from projective geometry.
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Cones were constructed by rotating a right triangle about one of its legs so the hypotenuse generates the surface of the cone (such a line is called a generatrix). Three types of cones were determined by their vertex angles (measured by twice the angle formed by the hypotenuse and the leg being rotated about in the right triangle). The conic section was then determined by intersecting one of these cones with a plane drawn perpendicular to a generatrix. The type of the conic is determined by the type of cone, that is, by the angle formed at the vertex of the cone: If the angle is acute then the conic is an ellipse; if the angle is right then the conic is a parabola; and if the angle is obtuse then the conic is a hyperbola (but only one branch of the curve).
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Nine-point hyperbola: One branch bisects BA, BC, and BP. The other branch bisects PA, PC, and AC, as well as passing through BA.PC and AP.BC. In plane geometry with triangle ABC, the nine-point hyperbola is an instance of the nine-point conic described by Maxime Bôcher in 1892. The celebrated nine-point circle is a separate instance of Bôcher's conic: :Given a triangle ABC and a point P in its plane, a conic can be drawn through the following nine points: :: the midpoints of the sides of ABC, :: the midpoints of the lines joining P to the vertices, and :: the points where these last named lines cut the sides of the triangle. The conic is an ellipse if P lies in the interior of ABC or in one of the regions of the plane separated from the interior by two sides of the triangle; otherwise, the conic is a hyperbola. Bôcher notes that when P is the orthocenter, one obtains the nine-point circle, and when P is on the circumcircle of ABC, then the conic is an equilateral hyperbola.
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The cap is initially conic in shape, and expands to hemispheric in maturity, typically reaching in diameter.
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The Haralson is a cultivar of apple that is medium-sized and has a round-conic shape.
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An instrument for drawing conic sections was first described in 1000 CE by the Islamic mathematician Al-Kuhi.
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The shell is imperforate, conic and globular. Whorls are convex. The spire is short. The peristome is continuous.
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The spire is conic. The apex is acute. The sutures are impressed. There are about seven, convex whorls.
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Pencils of circles: in the pencil of red circles, the only degenerate conic is the horizontal axis; the pencil of blue circles has three degenerate conics, the vertical axis and two circles of radius zero. The conic section with equation x^2-y^2 = 0 is degenerate as its equation can be written as (x-y)(x+y)= 0, and corresponds to two intersecting lines forming an "X". This degenerate conic occurs as the limit case a=1, b=0 in the pencil of hyperbolas of equations a(x^2-y^2) - b=0. The limiting case a=0, b=1 is an example of a degenerate conic consisting of twice the line at infinity. Similarly, the conic section with equation x^2 + y^2 = 0, which has only one real point, is degenerate, as x^2+y^2 is factorable as (x+iy)(x-iy) over the complex numbers.
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Conic optimization is a subfield of convex optimization that studies problems consisting of minimizing a convex function over the intersection of an affine subspace and a convex cone. The class of conic optimization problems includes some of the most well known classes of convex optimization problems, namely linear and semidefinite programming.
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In a pappian plane (i.e., a projective plane coordinatized by a field), if the field does not have characteristic two, a von Staudt conic is equivalent to a Steiner conic. However, R. Artzy has shown that these two definitions of conics can produce non-isomorphic objects in (infinite) Moufang planes.
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Some non-optical design references use the letter p as the conic constant. In these cases, p = K + 1\.
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In any case (parallel or central projection), the contour lines of quadrics are conic sections. See below and Umrisskonstruktion.
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What should be considered as a degenerate case of a conic depends on the definition being used and the geometric setting for the conic section. There are some authors who define a conic as a two-dimensional nondegenerate quadric. With this terminology there are no degenerate conics (only degenerate quadrics), but we shall use the more traditional terminology and avoid that definition. In the Euclidean plane, using the geometric definition, a degenerate case arises when the cutting plane passes through the apex of the cone.
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The shells of Amphidromus are relatively large, from one to three inches high, and colorful. Amphidromus has an elongate-conic or ovate-conic helicoid shell of 5 to 8 whorls. The shell may be thin and fragile, or very heavy and solid, with no known correlation of shell structure with distribution or habitats.
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Type species of the genus Achatinella is Achatinella apexfulva (Dixon). Subgenus Bulimella Pfeiffer, 1854: Shell shape is oblong-conic or ovate. The spire is obtuse, rounded or convexly-conic near the apex. The outer lip is thickened by a strong callous rib within the aperture (except in Achatinella abbreviata and Achatinella lila).
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An aconic reflector refers to a light energy reflector that is not defined by a mathematical equation. Most light energy reflectors are based on conic sections such as parabolas, ellipses and circles. Aconic reflector is a generic term used to explain a reflective curve outside these groups. It literally means not conic.
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He studied conic sections, cubic equations and problems of artillery. He is also known for solving the Cramer–Castillon problem.
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Apollonius of Perga (c. 262 BCE – c. 190 BCE) is mainly known for his investigation of conic sections. René Descartes.
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The problem was then considered unsolvable until 10th century Persian mathematician Abu Ja'far al-Khazin solved it using conic sections.
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The spire is conic. The apex is obtuse. The five whorls are subcarinate with sutures excavated. The aperture is rounded.
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A special case is Pascal's theorem, in which case the two cubics in question are all degenerate: given six points on a conic (a hexagon), consider the lines obtained by extending opposite sides – this yields two cubics of three lines each, which intersect in 9 points – the 6 points on the conic, and 3 others. These 3 additional points lie on a line, as the conic plus the line through any two of the points is a cubic passing through 8 of the points. A second application is Pappus's hexagon theorem, similar to the above, but the six points are on two lines instead of on a conic. Finally, a third case is found on the associativity of the group of elliptic curves.
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Elliptic case Hyperbolic case In geometry, the ', named for 18th century British mathematicians William Braikenridge and Colin Maclaurin, is the converse to Pascal's theorem. It states that if the three intersection points of the three pairs of lines through opposite sides of a hexagon lie on a line L, then the six vertices of the hexagon lie on a conic C; the conic may be degenerate, as in Pappus's theorem. The Braikenridge–Maclaurin theorem may be applied in the Braikenridge–Maclaurin construction, which is a synthetic construction of the conic defined by five points, by varying the sixth point. Namely, Pascal's theorem states that given six points on a conic (the vertices of a hexagon), the lines defined by opposite sides intersect in three collinear points.
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It touches the sides at its midpoints. There is no other (non-degenerate) conic section with the same properties, because a conic section is determined by 5 points/tangents. b) By a simple calculation. c) The circumcircle is mapped by a scaling, with factor 1/2 and the centroid as center, onto the incircle.
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These points cannot be covered by only, which gives us . Since degenerate conics are a union of at most two lines, there are always four out of seven points on a degenerate conic that are collinear. Consequently: :If no seven points out of lie on a non-degenerate conic, and no four points out of lie on a line, then the vector space of cubic homogeneous polynomials that vanish on (the affine cones of) has dimension two. On the other hand, assume are collinear and no seven points out of are co-conic.
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No continuous arc of a conic can be constructed with straightedge and compass. However, there are several straightedge-and-compass constructions for any number of individual points on an arc. One of them is based on the converse of Pascal's theorem, namely, if the points of intersection of opposite sides of a hexagon are collinear, then the six vertices lie on a conic. Specifically, given five points, and a line passing through , say , \a point that lies on this line and is on the conic determined by the five points can be constructed.
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Applying the degree formula above, the inverse of a conic (other than a circle) is a circular cubic if the center of inversion is on the curve, and a bicircular quartic otherwise. Conics are rational so the inverse curves are rational as well. Conversely, any rational circular cubic or rational bicircular quartic is the inverse of a conic. In fact, any such curve must have a real singularity and taking this point as a center of inversion, the inverse curve will be a conic by the degree formula.
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Aristaeus the Elder (; 370 – 300 BC) was a Greek mathematician who worked on conic sections. He was a contemporary of Euclid.
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It is also hairy. The seeds are ovoid, smooth, wrinkled or pitted. At one end there is a colorless, conic appendage.
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Balmaha sits at the westerly foot of Conic Hill, and is roughly along the West Highland Way if coming from Milngavie.
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The symmetry of point and line is expressed as projective duality. Starting with perspectivities, the transformations of projective geometry are formed by composition, producing projectivities. Steiner identified sets preserved by projectivities such as a projective range and pencils. He is particularly remembered for his approach to a conic section by way of projectivity called the Steiner conic.
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Conics, also known as conic sections to emphasize their three-dimensional geometry, arise as the intersection of a plane with a cone. Degeneracy occurs when the plane contains the apex of the cone or when the cone degenerates to a cylinder and the plane is parallel to the axis of the cylinder. See Conic section#Degenerate cases for details.
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P. chupaderae is a small snail that has a height of and an ovate-conic to elongate-conic, small to medium-sized shell. Its differentiated from other Pyrgulopsis in that its penial filament has a medium length lobe and medium length filament with the penial ornament consisting of an elongate penial gland; curved, transverse terminal gland; and ventral gland.
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The cap is initially conic or parabolic, but expands somewhat in maturity to become convex, and typically reaches dimensions of up to .
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When a conic is chosen for a projective range, and a particular point E on the conic is selected as origin, then addition of points may be defined as follows:Viktor Prasolov & Yuri Solovyev (1997) Elliptic Functions and Elliptic Integrals, page one, Translations of Mathematical Monographs volume 170, American Mathematical Society : Let A and B be in the range (conic) and AB the line connecting them. Let L be the line through E and parallel to AB. The "sum of points A and B", A + B, is the intersection of L with the range. The circle and hyperbola are instances of a conic and the summation of angles on either can be generated by the method of "sum of points", provided points are associated with angles on the circle and hyperbolic angles on the hyperbola.
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The better-known nine-point circle is an instance of Bôcher's conic. The nine-point hyperbola is another instance. Bôcher used the four points of the complete quadrangle as three vertices of a triangle with one independent point: :Given a triangle ABC and a point P in its plane, a conic can be drawn through the following nine points: :: the midpoints of the sides of ABC, :: the midpoints of the lines joining P to the vertices, and :: the points where these last named lines cut the sides of the triangle. The conic is an ellipse if P lies in the interior of ABC or in one of the regions of the plane separated from the interior by two sides of the triangle, otherwise the conic is a hyperbola.
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If is a conic this implies its dual is also a conic. This can also be seen geometrically: the map from a conic to its dual is one-to-one (since no line is tangent to two points of a conic, as that requires degree 4), and tangent line varies smoothly (as the curve is convex, so the slope of the tangent line changes monotonically: cusps in the dual require an inflection point in the original curve, which requires degree 3). For curves with singular points, these points will also lie on the intersection of the curve and its polar and this reduces the number of possible tangent lines. The degree of the dual given in terms of the d and the number and types of singular points of is one of the Plücker formulas.
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A degenerate case of Pascal's theorem (four points) is interesting; given points on a conic , the intersection of alternate sides, , , together with the intersection of tangents at opposite vertices and are collinear in four points; the tangents being degenerate 'sides', taken at two possible positions on the 'hexagon' and the corresponding Pascal line sharing either degenerate intersection. This can be proven independently using a property of pole-polar. If the conic is a circle, then another degenerate case says that for a triangle, the three points that appear as the intersection of a side line with the corresponding side line of the Gergonne triangle, are collinear. Six is the minimum number of points on a conic about which special statements can be made, as five points determine a conic.
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In these methods, it is considered that the body is always moving in a conic section, however the conic section is constantly changing due to the perturbations. If all perturbations were to cease at any particular instant, the body would continue in this (now unchanging) conic section indefinitely; this conic is known as the osculating orbit and its orbital elements at any particular time are what are sought by the methods of general perturbations. General perturbations takes advantage of the fact that in many problems of celestial mechanics, the two-body orbit changes rather slowly due to the perturbations; the two-body orbit is a good first approximation. General perturbations is applicable only if the perturbing forces are about one order of magnitude smaller, or less, than the gravitational force of the primary body.
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There are an infinitude of other curved shapes in two dimensions, notably including the conic sections: the ellipse, the parabola, and the hyperbola.
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The equidistant conic projection is a conic map projection commonly used for maps of small countries as well as for larger regions such as the continental United States that are elongated east-to-west. Also known as the simple conic projection, a rudimentary version was described during the 2nd century CE by the Greek astronomer and geographer Ptolemy in his work Geography. The projection has the useful property that distances along the meridians are proportionately correct, and distances are also correct along two standard parallels that the mapmaker has chosen. The two standard parallels are also free of distortion.
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According to Forrest, one possible impetus for a mathematical model for this process was the potential loss of the critical design components for an entire aircraft should the loft be hit by an enemy bomb. This gave rise to "conic lofting", which used conic sections to model the position of the curve between the ducks. Conic lofting was replaced by what we would call splines in the early 1960s based on work by J. C. Ferguson at Boeing and (somewhat later) by M.A. Sabin at British Aircraft Corporation. The word "spline" was originally an East Anglian dialect word.
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Hence for any line g the image \pi(g)=\pi_a\pi_b(g) can be constructed and therefore the images of an arbitrary set of points. The lines u and v contain only the conic points U and V resp.. Hence u and v are tangent lines of the generated conic section. A proof that this method generates a conic section follows from switching to the affine restriction with line w as the line at infinity, point O as the origin of a coordinate system with points U,V as points at infinity of the x- and y-axis resp. and point E=(1,1).
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The nine-point circle with the Euler line was generalized into the nine-point conic. Through a similar process, due to the analogous properties of the two circles, the Spieker circle was also able to be generalized into the Spieker conic. The Spieker conic is still found within the medial triangle and touches each side of the medial triangle, however it does not meet those sides of the triangle at the same points. If lines are constructed from each vertex of the medial triangle to the Nagel point, then the midpoint of each of those lines can be found.
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Most of the Southern Altaians traditionally lived in yurts. Many Northern Altaians mainly built polygonal yurts with conic roofs made out of logs and bark. Some Altai-Kizhi also lived in mud huts with birch bark gable roofs and log or plank walling. The Teleuts and a few Northern Altaians lived in conic homes made out of perches or bark.
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In 1772 he created the Lambert conformal conic and Lambert azimuthal equal-area projections. The Albers equal-area conic projection features no distortion along standard parallels. It was invented by Heinrich Albers in 1805. In 1715 Herman Moll published the Beaver Map, one of the most famous early maps of North America, which he copied from a 1698 work by Nicolas de Fer.
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The shells of Liguus are more slender than those of Orthalicus, the only other orthalicine genus with which it is likely to be confused. The shape of Liguus shells is characterized by Pilsbry as "oblong-conic", versus "ovate-conic" for Orthalicus. Generally recognized Florida subspecies of Liguus fasciatus (from Pilsbry, 1912), left to right: Liguus fasciatus castaneozonatus, L. f. elliottensis, L. f.
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The dual can be visualized as a locus in the plane in the form of the polar reciprocal. This is defined with reference to a fixed conic as the locus of the poles of the tangent lines of the curve . The conic is nearly always taken to be a circle and this case the polar reciprocal is the inverse of the pedal of .
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Construct three lines da, db, dc through P such that they meet the conic at A, A'; B, B' ; C, C' respectively. Let D be a point on the polar of point P with respect to (S) or D lies on the conic (S). Let DA' ∩ BC =A0; DB' ∩ AC = B0; DC' ∩ AB= C0. Then A0, B0, C0 are collinear.
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The conic sections have been studied for thousands of years and have provided a rich source of interesting and beautiful results in Euclidean geometry.
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In Euclidean and projective geometry, just as two (distinct) points determine a line (a degree-1 plane curve), five points determine a conic (a degree-2 plane curve). There are additional subtleties for conics that do not exist for lines, and thus the statement and its proof for conics are both more technical than for lines. Formally, given any five points in the plane in general linear position, meaning no three collinear, there is a unique conic passing through them, which will be non-degenerate; this is true over both the Euclidean plane and any pappian projective plane. Indeed, given any five points there is a conic passing through them, but if three of the points are collinear the conic will be degenerate (reducible, because it contains a line), and may not be unique; see further discussion.
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The horopter was then used by architect Girard Desargues, who in 1639 published a remarkable treatise on the conic sections, emphasizing the idea of projection.
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The extension from a circle to a conic having center: The creative method of new theorems, International Journal of Computer Discovered Mathematics, pp.21-32.
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The Lambert conformal conic is one of several map projection systems developed by Johann Heinrich Lambert, an 18th-century Swiss mathematician, physicist, philosopher, and astronomer.
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Thus, a polarity relates a point with a line and, following Gergonne, is called the polar of and the pole of . An absolute point (line) of a polarity is one which is incident with its polar (pole).Coxeter and several other authors use the term self-conjugate instead of absolute. A von Staudt conic in the real projective plane is equivalent to a Steiner conic.
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If these points are real, the curve is a hyperbola; if they are imaginary conjugates, it is an ellipse; if there is only one double point, it is a parabola. If the points at infinity are the cyclic points and , the conic section is a circle. If the coefficients of a conic section are real, the points at infinity are either real or complex conjugate.
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Planes that pass through the vertex of the cone will intersect the cone in a point, a line or a pair of intersecting lines. These are called degenerate conics and some authors do not consider them to be conics at all. Unless otherwise stated, "conic" in this article will refer to a non-degenerate conic. There are three types of conics: the ellipse, parabola, and hyperbola.
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Cupressus arizonica is a coniferous evergreen tree with a conic to ovoid-conic crown. It grows to heights of 10–25 m (32.8-82.0 ft), and its trunk diameter reaches 0.5 m (19.7 in). The foliage grows in dense sprays, varying from dull gray-green to bright glaucous blue-green. The leaves are scale-like, 2–5 mm long, and produced on rounded (not flattened) shoots.
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The shell is umbilicated, ovate, conic above, moderately solid, brown with a buff line at the periphery, very delicately sculptured with lines of growth, and sometimes has low wrinkles and fine impressed spiral striae. The spire of the shell is conic. The apex is obtuse. The sculpture of the nepionic whorls (the whorls immediately following the embryonic whorls) has superficial vermiculate (worm-like) wrinkles.
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His mathematical works were in the areas of spherical trigonometry, as well as conic sections. He published an original work on conic sections in 1522 and is one of several mathematicians sometimes credited with the invention of prosthaphaeresis, which simplifies tedious computations by the use of trigonometric formulas, sometimes called Werner's formulas.Howard Eves, An Introduction to the History of Mathematics, Sixth Edition, p. 309, Thompson, 1990, .
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The solid shell grows to a height of 2 cm and has an ovate- conic shape. Its pointed, conic spire is higher and more acute than the spire of Phasianella nivosa. The five, somewhat convex whorls are separated by well marked sutures and are somewhat flattened above. The rather small aperture is short ovate, and measures less than half the length of the shell.
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Two distinct secant lines to the conic, say and determine four points on the conic () that form a quadrangle. The point is a vertex of the diagonal triangle of this quadrangle. The polar of with respect to is the side of the diagonal triangle opposite . The theory of projective harmonic conjugates of points on a line can also be used to define this relationship.
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In 1655, Wallis published a treatise on conic sections in which they were defined analytically. This was the earliest book in which these curves are considered and defined as curves of the second degree. It helped to remove some of the perceived difficulty and obscurity of René Descartes' work on analytic geometry. In the Treatise on the Conic Sections Wallis popularised the symbol ∞ for infinity.
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The Kumandins were originally hunters and animals living in the taiga were vital to the local subsistence economy. The traditional dwellings of the Kumandins included polygonal yurts made out of bark or log and topped with a conic bark roof. Other types of dwellings also included conic yurts made out of bark or perches. Traditional Kumandin dress included short breeches, linen shirts, and single-breasted robes.
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The Tubalars were originally hunters and animals living in the taiga were vital to the local subsistence economy. The traditional dwellings of the Tubalars included polygonal yurts made out of bark or log and topped with a conic bark roof. Other types of dwellings also included conic yurts made out of bark or perches. Traditional Tubalar dress included short breeches, linen shirts, and single-breasted robes.
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Diagram from Apollonius' Conics, in a 9th-century Arabic translation The greatest progress in the study of conics by the ancient Greeks is due to Apollonius of Perga (died c. 190 BCE), whose eight-volume Conic Sections or Conics summarized and greatly extended existing knowledge.Apollonius of Perga, Treatise on Conic Sections, edited by T. L. Heath (Cambridge: Cambridge University Press, 2013). Apollonius's study of the properties of these curves made it possible to show that any plane cutting a fixed double cone (two napped), regardless of its angle, will produce a conic according to the earlier definition, leading to the definition commonly used today.
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While five points determine a conic, sets of six or more points on a conic are not in general position, that is, they are constrained as is demonstrated in Pascal's theorem. Similarly, while nine points determine a cubic, if the nine points lie on more than one cubic--i.e., they are the intersection of two cubics--then they are not in general position, and indeed satisfy an addition constraint, as stated in the Cayley–Bacharach theorem. Four points do not determine a conic, but rather a pencil, the 1-dimensional linear system of conics which all pass through the four points (formally, have the four points as base locus).
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James Ivory, FRS FRSE KH LLD (17 February 1765 – 21 September 1842) was a British mathematician. He was creator of Ivory's Theorem on confocal conic sections.
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The height of the shell reaches 6.2 mm. The elongate shell has a pointed ovate shape. It is thin, smooth, and shining. The spire is conic.
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Ptolemy projected two different types of maps in his text. The first, known as a conic projection, dealt with the latitude parallels consisting of round arcs.
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The circle is an instance of a conic section and the nine-point circle is an instance of the general nine-point conic that has been constructed with relation to a triangle ABC and a fourth point P, where the particular nine-point circle instance arises when P is the orthocenter of ABC. The vertices of the triangle and P determine a complete quadrilateral and three "diagonal points" where opposite sides of the quadrilateral intersect. There are six "sidelines" in the quadrilateral; the nine-point conic intersects the midpoints of these and also includes the diagonal points. The conic is an ellipse when P is interior to ABC or in a region sharing vertical angles with the triangle, but a nine-point hyperbola occurs when P is in one of the three adjacent regions, and the hyperbola is rectangular when P lies on the circumcircle of ABC.
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The converse is the Braikenridge–Maclaurin theorem, named for 18th- century British mathematicians William Braikenridge and Colin Maclaurin , which states that if the three intersection points of the three pairs of lines through opposite sides of a hexagon lie on a line, then the six vertices of the hexagon lie on a conic; the conic may be degenerate, as in Pappus's theorem. The Braikenridge–Maclaurin theorem may be applied in the Braikenridge–Maclaurin construction, which is a synthetic construction of the conic defined by five points, by varying the sixth point. The theorem was generalized by August Ferdinand Möbius in 1847, as follows: suppose a polygon with sides is inscribed in a conic section, and opposite pairs of sides are extended until they meet in points. Then if of those points lie on a common line, the last point will be on that line, too.
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A fundamental application is that, in the plane, five points determine a conic, as long as the points are in general linear position (no three are collinear).
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Perseus (; c. 150 BC) was an ancient Greek geometer, who invented the concept of spiric sections, in analogy to the conic sections studied by Apollonius of Perga.
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Unlike other conic projections, no true secant form of the projection exists because using a secant cone does not yield the same scale along both standard parallels.
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The seed coat is crustaceous, mostly with papillose, conic outgrowths along one side. The vertical embryo is curved (comma-shaped). The seed contains copious perisperm (feeding tissue).
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Parrilo and A. Jadbabaie. "Approximation of the joint spectral radius using sum of squares." Linear Algebra and its Applications, 428(10):2385–2402, 2008. and conic programming.
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To distinguish the degenerate cases from the non-degenerate cases (including the empty set with the latter) using matrix notation, let be the determinant of the 3×3 matrix of the conic section—that is, ; and let be the discriminant. Then the conic section is non-degenerate if and only if . If we have a point when , two parallel lines (possibly coinciding) when , or two intersecting lines when .
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A sharply angled plane with an offset conic section removed was chosen as the most efficient. With this configuration, the head first separated (by force) the sediments to be displaced while supporting the sediments of the bore wall. A vortex of water was created by angled water jets in the conic space. This design massively disturbed sediments in one ‘exhaust’ sector of the SPI image, but minimised disturbance in the remainder.
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The size of the shell varies between 6 mm and 10 mm. The narrowly umbilicate shell has a globose- conic shape with a conic spire and an acute apex. It is pinkish, dark brown, blackish or pink, radiately maculated with white below the sutures, and dotted with white around the center of the base. The 5 to 6 whorls are convex and separated by canaliculate sutures, and spirally granose-lirate.
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The Chelkans were originally hunters and animals living in the taiga were their main prey and were vital to the local subsistence economy. The Chelkans traditional dwellings included polygonal yurts made out of bark or log and topped with a conic bark roof. Other types of dwellings also included conic yurts made out of bark or perches. Traditional Chelkan dress included short breeches, linen shirts, and single-breasted robes.
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It is a tree growing to tall, with a broad conic crown and a trunk up to diameter. The shoots are stout, pale yellow-brown, hairless or slightly hairy. The leaves are linear, long and wide, glossy green above, and with two white stomatal bands below. The cones are narrow cylindric-conic, bright green when immature, ripening pale yellow-brown, long and wide, with exserted and reflexed bracts.
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Hyperbolas may be seen in many sundials. On any given day, the sun revolves in a circle on the celestial sphere, and its rays striking the point on a sundial traces out a cone of light. The intersection of this cone with the horizontal plane of the ground forms a conic section. At most populated latitudes and at most times of the year, this conic section is a hyperbola.
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The slender, yellowish-brown shell has an elongate-conic shape. Its outline is almost rectilinear. It has a polished appearance. The length of the shell measures 4.2 mm.
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The large, solid, imperforate shell has a conic shape. The periphery is carinated. The base of the shell is flattened. The umbilical tract shows a strong curved rib.
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The shell grows to a height of 3.8 mm. The elongate shell has a pointed ovate shape. It is rather thin, smooth, and shining. The spire is conic.
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Calyx teeth obsolete or minute. Stylopodium conic; styles 3–4 times longer than stylopodium. Fruit ovoid, 1.5–3 × 1–2 mm; lateral ribs slightly broader than the dorsal.
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The spire is conic. The 6 to 7 whorls are convex. The apex is usually eroded and orange-colored. The body whorl is flattened around the superior portion.
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The three carpels are at first distinct and become indistinct. The three styles are long. The capsule is conic-ellipsoid, measuring long and wide. The seeds are long.
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Every smooth projective curve X of genus zero over a field k is isomorphic to a conic (degree 2) curve in P2. If X has a k-rational point, then it is isomorphic to P1 over k, and so its k-rational points are completely understood.Hindry & Silverman (2000), Theorem A.4.3.1. If k is the field Q of rational numbers (or more generally a number field), there is an algorithm to determine whether a given conic has a rational point, based on the Hasse principle: a conic over Q has a rational point if and only if it has a point over all completions of Q, that is, over R and all p-adic fields Qp.
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The small shell has an elongate-conic shape. It has a smooth appearance, except for incremental lines. The suture is distinct but not deep. The apical portion is decollate.
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He wrote this treatise in Cairo. It was translated into French by J. J. Sedillot in 1834. He also the author of Kitab al-Kotua al-Makhrutia (conic sections).
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The round beads are distinct. The base of the shell has about 10 scarcely granulous concentric lirae. The outlines of the conic spire are straight. The apex is acute.
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The shell size varies between 3 mm and 6 mm. The short and solid shell has an oval or ovate shape. The spire is conic. The apex is obtuse.
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The semitransparent, bluish white shell has an elongate-conic shape. Its length measures 3.8 mm. There are at least two whorls in the protoconch. These are 2, well rounded.
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Woltman 2007, pp. 332–334 While most such thin films lase on the axis normal to the film's surface, some will lase on a conic angle around that axis.
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This shows that pole and polar line are concepts in the projective geometry of the plane and generalize with any nonsingular conic in the place of the circle C.
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The milk-white shell has an elongate-conic shape. Its length measures 6.1 mm. (The whorls of the protoconch aredecollated). The eleven whorls of the teleoconch are well rounded.
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The shell has an elongate-conic shape. Its length measures .39 inch. The teleoconch contains 15 whorls that are moderately convex and are marked by a well impressed suture.
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It is accessible for walking, and forms part of the West Highland Way. During the lambing season, dogs are not allowed in the two enclosed fields on the east approach to Conic Hill, even if they are on a lead. The season normally lasts for around three weeks at the end of April and early May. However, this does not affect access with a dog to Conic Hill from the Balmaha direction.
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If there is an intersection point of multiplicity at least 3, the two curves are said to be osculating. If there is only one intersection point, which has multiplicity 4, the two curves are said to be superosculating.. Furthermore, each straight line intersects each conic section twice. If the intersection point is double, the line is a tangent line. Intersecting with the line at infinity, each conic section has two points at infinity.
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The length of the shell varies between 25 mm and 86 mm. The short, solid, imperforate shell has an ovate-conic shape with a conic spire. Its color pattern is olivaceous, green, brown or grayish, longitudinally strigate or tessellate with white. The five whorls are generally angulate and nodose at the shoulder, with a varying number of coarse subnodose revolving carinae and of intermediate lirulae upon the median and lower portions of the body whorl.
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The second theorem is that for any conic section, the distance from a fixed point (the focus) is proportional to the distance from a fixed line (the directrix), the constant of proportionality being called the eccentricity. A conic section has one Dandelin sphere for each focus. An ellipse has two Dandelin spheres touching the same nappe of the cone, while hyperbola has two Dandelin spheres touching opposite nappes. A parabola has just one Dandelin sphere.
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Pascal's original note has no proof, but there are various modern proofs of the theorem. It is sufficient to prove the theorem when the conic is a circle, because any (non-degenerate) conic can be reduced to a circle by a projective transformation. This was realised by Pascal, whose first lemma states the theorem for a circle. His second lemma states that what is true in one plane remains true upon projection to another plane.
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The spire is conic and eroded. The sutures are linear and impressed. The five whorls are convex and spirally grooved. These grooves are shallow, about 5 on the penultimate whorl.
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The spiral riblets are rufous or pinkish brown. The spire is conoidal with an acute apex. The sides are slightly convex. The small protoconch is conic with about 2 whorls.
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The shell of this species is large, solid, thick and imperforate. The shape of the shell is obtusely conic. The spire is elevated. The whorls are flattened, nodulous and carinated.
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The very regularly elongate conic shell is umbilicated, yellowish white. It measures 5.2 mm. The whorls of the protoconch are decollated. The six whorls of the teleoconch are moderately rounded.
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The yellowish-white shell has an elongate conic shape. Its length measures 9 mm. The whorls of the protoconch are decollated. The nine whorls of the teleoconch are almost flattened.
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The shape of the shell is ovate-conic. The shell is thick and smooth. The smooth shell is unique in the tribe Jullieniini. The outer lip is thick with growth lines.
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Domenico Alfonso Emmanuele Montesano (Potenza, 22 December 1863 - Naples, 1 October 1930) was an Italian mathematician. He influenced and developed the theory on linear congruences and on the conic bilinear complexes.
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Adults can measure up to 15 cm, tail included. Robust body and flat head. Back, legs and tail with prominent conic tubercles. Its regenerated tail is smoother and doesn't have tubercles.
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The length of the shell varies between 50 mm and 90 mm. The large, imperforate, rather thin shell is conic. The periphery is rounded. The spire is more or less elevated.
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The height of the shell attains 14 mm. The light-yellow turreted-conic shell is narrowly umbilicate. The eight whorls are nearly plane. They are encircled by numerous unequal granuliferous riblets.
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The size of the shell attains 90 mm. The large, imperforate shell has a depressed-conic shape. It is pale yellowish. The six whorls are planulate above, and obliquely tuberculate-plicate.
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Hieronymus Georg Zeuthen (15 February 1839 – 6 January 1920) was a Danish mathematician. He is known for work on the enumerative geometry of conic sections, algebraic surfaces, and history of mathematics.
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In the same way, the special affine curvature of a curve at a point is the special affine curvature of its hyperosculating conic, which is the unique conic making fourth order contact (having five point contact) with the curve at . In other words it is the limiting position of the (unique) conic through and four points on the curve, as each of the points approaches : :P_1,P_2,P_3,P_4\to P. In some contexts, the affine curvature refers to a differential invariant of the general affine group, which may readily obtained from the special affine curvature by , where is the special affine arc length. Where the general affine group is not used, the special affine curvature is sometimes also called the affine curvature .
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Let meet in , meet in and let meet at . Then meets at the required point . By varying the line through ,as many additional points on the conic as desired can be constructed. Parallelogram method for constructing an ellipse Another method, based on Steiner's construction and which is useful in engineering applications, is the parallelogram method, where a conic is constructed point by point by means of connecting certain equally spaced points on a horizontal line and a vertical line.
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Dandelin spheres are touching the pale yellow plane that intersects the cone.In geometry, the Dandelin spheres are one or two spheres that are tangent both to a plane and to a cone that intersects the plane. The intersection of the cone and the plane is a conic section, and the point at which either sphere touches the plane is a focus of the conic section, so the Dandelin spheres are also sometimes called focal spheres.Taylor, Charles.
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Albers projection of the world with standard parallels 20°N and 50°N. The Albers projection with standard parallels 15°N and 45°N, with Tissot's indicatrix of deformation An Albers projection shows areas accurately, but distorts shapes. The Albers equal-area conic projection, or Albers projection (named after Heinrich C. Albers), is a conic, equal area map projection that uses two standard parallels. Although scale and shape are not preserved, distortion is minimal between the standard parallels.
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Also, the midpoints of each side of the medial triangle are found and connected to the midpoint of the opposite line through the Nagel point. Each of these lines share a common midpoint, S. With each of these lines reflected through S, the result is 6 points within the medial triangle. Draw a conic through any 5 of these reflected points and the conic will touch the final point. This was proven by de Villiers in 2006.
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Cupressus lusitanica is an evergreen conifer tree with a conic to ovoid-conic crown, growing to 40 m tall. The foliage grows in dense sprays, dark green to somewhat yellow-green in colour. The leaves are scale-like, 2–5 mm long, and produced on rounded (not flattened) shoots. The seed cones are globose to oblong, 10–20 mm long, with four to 10 scales, green at first, maturing brown or grey-brown about 25 months after pollination.
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The solid shell is imperforate and depressed globose. It is slate-colored or black, sometimes (especially if worn) reddish or brownish. The conic spire is short. The apex is acute, usually reddish.
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The laterals are of the usual form and bear cusps. The imperforate shell has a turbinate shape. The spire is conic with whorls rounded at the periphery. The upper whorls are spiny.
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The small shell is depressed and conic. Its color is yellowish, variegated and articulated with rose-pink and opaque white. The 4 to 5 whorls are rounded. The minute nucleus is smooth.
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The shell has a broadly, elongate-conic shape. Its length measures 6.1 mm. Its color is bright brown, excepting the protoconch, which is white. The 2½ whorls of the protoconch are planorboid.
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The shell grows to a height of 4 mm. The umbilicate, rather thick, whitish, subvitreous shell has a conic-depressed shape. The apex is obtuse. The first 3 whorls are planate above.
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The semitranslucent, bluish-white shell is small and has an elongate-conic shape. Its length measures 2.1 mm. The whorls of the protoconch number at least two. They are large and smooth.
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The last whorl is about as long as the spire. The suture is impressed. The spire is conic and acute. Aperture is little oblique, oblong, with a very pale lilac border within.
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Azucaron pineapples (also called azucaron) are very sweet pineapples found in Honduras and other parts of central and South America. Is quite resistant to droughts and its fruit is of conic shape.
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9, p.212 identified in Johannes Werner's 16th-century manuscript on conic sections. Now recognized as one of Werner's formulas, it was essential for the development of prosthaphaeresis and logarithms decades later.
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In February 1983, Conic Semiconductor, was acquired from Honic, the unlisted portion of the larger Conic Group, for HK$55 million cash. The subsidiary was the largest producer of liquid-crystal display panel in Hong Kong according to the narrative of the company. However, in 1982, in order to cover a financial loss, Alex Au (Au Yan Din; ), chairman and the majority shareholder of Conic Investment at that time, invited Chinese state-owned enterprise (SOE) China Resources to subscribe a capital increase of the company (which an agreement was signed in January 1984 for 100 million number of new shares for HK$1 each), via a subsidiary Sin King Enterprises Company Limited (), as well as purchase 80 million number of shares from Au. After the completion of the capital increase, China Resources and Bank of China Group (at that time as unincorporated group of companies) became the controlling shareholder in 1984 for 35% ordinary shares via Sin King. Conic at that time declared that the company did not faced any difficulties, thus the takeover was not related to the situation of the company.
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The turreted-conic shell is imperforate. The whorls are convex. They are ornamented with granose cinguli, with two larger more prominent cinguli at the base of the shell. The interstices are longitudinally striate.
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The height of the shell attains 32 mm, its diameter 38 mm. The broad, rather solid shell has a conical shape. The spire is conic. The apex is generally eroded, corneous (orange colored).
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The imperforate, solid shell has an elevated-conic shape. It is longitudinally subobliquely crinkled. Its color pattern is reddish orange, marked in places with white and olivaceous. The suture is impressed and irregular.
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The small shell has an elongate conic shape. Its length measures 4.3 mm. It has a pale brown ground color, with the incised spiral lines red. The whorls of the protoconch are decollated.
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The conic spire is shorter and less attenuated than in Phasianotrochus bellulus. The about 7 whorls are scarcely convex. The body whorl is not carinate. It is finely striate beneath,and smooth above.
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The shape of the shell is ovate-conic. The apex is acute and violet-black in colour. The umbilicus of the shell is very narrow. There are fine spiral lines on the shell.
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The bluish-white shell has an elongate-conic shape. Its length measures 4.4 mm. The whorls in protoconch number more than two. They are smooth, the early portion obliquely immersed in the later.
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The center of mass of a conic solid of uniform density lies one-quarter of the way from the center of the base to the vertex, on the straight line joining the two.
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The elongate-conic shell is bluish-white. It measures 2.9 mm. The whorls of the protoconch are decollated. The seven whorls of the teleoconch are very slightly rounded, separated by deeply channeled sutures.
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The size of the shell attains 24 mm. The imperforate shell has an ovate-conic shape. Its color pattern is yellowish brown, or yellow clouded with orange-brown. The elevated spire is acute.
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The size of the shell varies between 25 mm and 40 mm. The solid, imperforate shell has an elevated- conic shape. Its color pattern is olive-brown or cinereous. The apex is acute.
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Cupressus guadalupensis is an evergreen conifer tree with a conic to ovoid-conic crown, variable in size, with mature trees reaching tall. The foliage grows in dense sprays, dark green to gray-green in color. The leaves are scale-like, 2–5 mm long, and produced on rounded (not flattened) shoots. The seed cones are spherical to oblong, 12–35 mm long, with 6 to 10 scales, green at first, maturing gray-brown to gray about 20–24 months after pollination.
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The American polyconic projection can be thought of as "rolling" a cone tangent to the Earth at all parallels of latitude. This generalizes the concept of a conic projection, which uses a single cone to project the globe onto. By using this continuously varying cone, each parallel becomes a circular arc having true scale, contrasting with a conic projection, which can only have one or two parallels at true scale. The scale is also true on the central meridian of the projection.
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In mathematics, an equidistant set (also called a midset, or a bisector) is a set each of whose elements has the same distance (measured using some appropriate distance function) from two or more sets. The equidistant set of two singleton sets in the Euclidean plane is the perpendicular bisector of the segment joining the two sets. The conic sections can also be realized as equidistant sets. This property of conics has been used to generalize the notion of conic sections.
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This brought him great support among the peasant population but not among all of the church hierarchy. After nearly thirteen years as a catechist, the gap between Choc's liberation theology and the conservative doctrine of many of his superiors became too large. Choc was hired by the National Indigenous and Peasant Coordinating Committee (CONIC) as a "promoter", working primarily with indigenous communities involved in land struggles. With CONIC, Choc earned a reputation for his firm defense of the rights of indigenous communities.
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Another technique to select and manipulate objects in 3D virtual spaces consists in pointing at objects using a virtual-ray emanating from the virtual hand. When the ray intersects with the objects, it can be manipulated. Several variations of this technique has been made, like the aperture technique, which uses a conic pointer addressed for the user's eyes, estimated from the head location, to select distant objects. This technique also uses a hand sensor to adjust the conic pointer size.
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The shell is small, bluish-white, and semi-translucent. It has a very irregularly elongate-conic shape. The early whorls are decollated. The four remaining whorls are almost flattened, and appressed at the summit.
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A significant portion of the vehicle's flight (other than immediate proximity to the Earth or Moon) requires accurate solution as a three-body problem, but may be preliminarily modeled as a patched conic approximation.
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The length of the shell attains 23 mm, its width 8 mm. (Original description) The shell is rather large and solid, cylindro-conic, tapering evenly. It contains 10 whorls. Its colour is uniform grey.
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The ovate-conic shell is perforate, solid, and shining. The sutures are impressed. The 5-6 whorls are convex, rounded, and spirally lirate. The body whorl exceeds the balance of the shell in length.
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The size of the shell varies between 13 mm and 15 mm. The shell has a depressed-conic shape. It is dark brown, adorned with colored bands with granules. The interstices are longitudinally elevated.
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The size of the shell varies between 19 mm and 45 mm. The solid, imperforate shell has a conical shape. It is russet-yellow, brown, orange-colored or deep crimson. The spire is conic.
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The size of the shell attains 14 mm. (Original description) The solid shell is much eroded. It is short, chalky, with an olive-gray periostracum and over five whorls. The short spire is conic.
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The color of the shell is bright scarlet-rose, the uppermost part of the whorls is white-zoned.George Washington Tryon, Manual of Conchology vol. VI, p. 233; 1884 The shell has an elongate-conic shape.
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The shell grows to a length of 13 mm. The pale wax-yellow shell has an elongate-conic shape. The sides of the spire are rectilinear in outline. The whorls of the protoconch are decollated.
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Seseli is a genus of herbaceous perennial plants. They are sometimes woody at base with a conic taproot. Leaf blades are 1–3-pinnate or pinnately decompound. Umbels are compound, with bracts few or absent.
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The type species is Gurmatia wilkinsi Dance & Eames, 1966. This is a small shell. It is ovate- conic in outline, thin and translucent. The protoconch is smooth, heterostrophic and obliquely immersed in the succeeding whorl.
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The length of the shell varies between 20 mm and 50 mm. The solid, umbilicate shell has a pointed- ovate shape. Its color pattern is greenish, longitudinally flammulated with black. The conic spire is pointed.
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The shape of the shell is ovate conic. The width of the shell is 14 mm; the height of the shell is 17 mm.Brown D. S. (1994). Freshwater Snails of Africa and their Medical Importance.
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Autumn foliage Willow oaks can grow moderately fast (height growth up to a year), and tend to be conic to oblong when young, rounding out and gaining girth at maturity (i.e. more than 50 years).
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Together they worked on free fall, catenary, conic section, and fluid statics. Both believed that it was necessary to create a method that thoroughly linked mathematics and physics.Durandin, Guy. 1970. Les Principes de la Philosophie.
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The slender, milk- white shell has an elongate-conic shape. The length of the shell measures between 7.5 mm and 10 mm. The protoconch contains three whorls. These are large, helicoid, rather elevated, and smooth.
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Hesperocyparis goveniana is an evergreen tree with a conic to ovoid-conic crown, very variable in size, with mature trees of under on some sites, to tall in ideal conditions. The foliage grows in dense sprays, dark green to somewhat yellow-green in color. The leaves are scale-like, long, and produced on rounded (not flattened) shoots. The seed cones are globose to oblong, long, with 6 to 10 scales, green at first, maturing brown or gray-brown about 20–24 months after pollination.
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The conic consists thus of two complex conjugate lines that intersect in the unique real point, (0,0), of the conic. The pencil of ellipses of equations ax^2+b(y^2-1)=0 degenerates, for a=0, b=1, into two parallel lines and, for a=1, b=0, into a double line. The pencil of circles of equations a(x^2+y^2-1) - bx =0 degenerates for a=0 into two lines, the line at infinity and the line of equation x=0.
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China Aerospace International Holdings Ltd. was previously known as Conic Investment Co., Ltd. (). It was incorporated on 25 July 1975 in British Hong Kong.Filings in Hong Kong Companies Registry It was acted as the holding company of Conic Group (), which including Cony Electronic Products (, incorporated in 1973), Chee Yuen Industrial Company (incorporated in 1969 and was majority owned by Alex Au), Far East United Electronics (incorporated in 1970), Grand Precision Works, Electric Company, Hong Yuen Electronics, Soundic Electronics, as well as other electronic and plastic manufacturers.
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La Hire wrote on graphical methods, 1673; on conic sections, 1685; a treatise on epicycloids, 1694; one on roulettes, 1702; and, lastly, another on conchoids, 1708. His works on conic sections and epicycloids were based on the teaching of Desargues, of whom he was the favourite pupil. He also translated the essay of Manuel Moschopulus on magic squares, and collected many of the theorems on them which were previously known; this was published in 1705. He also published a set of astronomical tables in 1702.
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The size of the shell attains 4 mm. The small, solid shell has a short ovate-conic shape. it is imperforate or narrowly umbilicate. It is white with numerous revolving series of red or brown tessellations.
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The length of the shell attains 25 mm, its diameter 8 mm. (Original description) The large, solid shell has an elongate-conic shape and is regularly tapering. Its colour is cinnamonbrown. The shell contains 10 whorls .
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The shell has a gently and evenly tapering, elongate-conic shape. It has a flesh-color with a brown base. Its length varies between 10 mm and 17 mm. The whorls of the protoconch are decollated.
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The height of the shell varies between 6 mm and 10 mm. Its color is red, ashen or purple. The small, globose shell is very solid and imperforate. The spire is conic, more or less depressed.
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The height of the shell attains 33 mm, its diameter 32 mm. The umbilicate, heavy, solid shell has a conic shape. It is chocolate-colored or brownish-olivaceous. The conical spire is more or less elevated.
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The length of the shell varies between 25 mm and 45 mm. The imperforate, solid shell has an elate-conic shape. Its color pattern is pale yellowish. The spire is elevated and contains 7–8 whorls.
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The size of the shell varies between 5 mm and 15 mm. The umbilicate shell has a conic-globose shape. It is maculate with white on a ground of reddish carmine. The five whorls are convex.
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The size of the shell varies between 6 mm and 18 mm. The imperforate, solid shell has a globose- conic shape. It is pinkish, with sparsely scattered reddish or blackish dots. The elevated spire is conical.
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The height of the shell reaches 8 mm. The small, solid, white, very minutely perforated shell has a globose-conic shape. The spire is short. The four whorls are convex and encircled by strong spiral ribs.
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The shell has a rounded and broad spire that pinches in steeply at the apex. The spire short, conic, very small compared with the body whorl. There are 4–5 whorls with deep sutures between them.
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The size of the shell varies between 20 mm and 25 mm. The conic shell is imperforate. The five whorls are flattened and subgranosely densely lirate. The periphery is carinated, armed with compressed imbricated subdeflexed spines.
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The short, yellowish white shell has a conic shape. (The whorls of the protoconch of the type specimen are eroded). Its length measures 5.6 mm. The 5½ whorls of the teleoconch are well rounded, slightly overhanging.
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The length of the species attains 15.3 mm, its diameter 5.7 mm. (Original description) The elongate-conic shell is flesh colored. The protoconch contains more than one, smooth whorl. The whorls of the teleoconch are strongly rounded.
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The swift upper reaches of rivers, which occasionally overflow and cause flooding and landslides, generally cut deeply into the conic slopes. By contrast, many of the water courses in the lowlands tend to be sluggish and meandering.
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The white, shiny shell has ta slender, elongate-conic shape. The length of the shell varies between 1.8 mm and 1.8 mm. The whorls of the protoconch are helicoid. The teleoconch contains 4½ to 5 flat whorls.
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The sculpture also becomes obsolescent toward the termination of the body whorl. The conic spire is small and acute. The sutures are subcanaliculate, with a beaded border. The 5½-6 whorls are quite convex, and rapidly increasing.
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The size of the shell varies between 5 mm and 12 mm. The imperforate, small, thick and solid shell has a globose-conic shape. It is blackish and unicolored. The conical spire is elevated or rather depressed.
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The brownish yellow shell has an elongate-conic shape. Its length measures 5 mm. (The whorls of the protoconch are decollated). The 7½ whorls of the teleoconch are very slightly rounded, and feebly shouldered at the summit.
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Leptoxis compacta lectotype. Scale bar is 5 mm. This species was originally described by the American naturalist and malacologist John Gould Anthony in 1854. The shell of Leptoxis compacta is ovate-conic, smooth, thick and yellowish-green.
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J. W. Downs, Practical Conic Sections, Dover Publ., 2003 (orig. 1993): p. 26. Let f be the distance from the vertex V (on both the hyperbola and its axis through the two foci) to the nearer focus.
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The problem of intersection of an ellipse/hyperbola/parabola with another conic section leads to a system of quadratic equations, which can be solved in special cases easily by elimination of one coordinate. Special properties of conic sections may be used to obtain a solution. In general the intersection points can be determined by solving the equation by a Newton iteration. If a) both conics are given implicitly (by an equation) a 2-dimensional Newton iteration b) one implicitly and the other parametrically given a 1-dimensional Newton iteration is necessary.
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Naïve application of dimension counting and Bézout's theorem yields incorrect results, as the following example shows. In response to these problems, algebraic geometers introduced vague "fudge factors", which were only rigorously justified decades later. As an example, count the conic sections tangent to five given lines in the projective plane. The conics constitute a projective space of dimension 5, taking their six coefficients as homogeneous coordinates, and five points determine a conic, if the points are in general linear position, as passing through a given point imposes a linear condition.
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The points of intersection, for will be points of the ellipse between and . The labeling associates the lines of the pencil through with the lines of the pencil through projectively but not perspectively. The sought for conic is obtained by this construction since three points and and two tangents (the vertical lines at and ) uniquely determine the conic. If another diameter (and its conjugate diameter) are used instead of the major and minor axes of the ellipse, a parallelogram that is not a rectangle is used in the construction, giving the name of the method.
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The black boundaries of the colored regions are conic sections. Not shown is the other half of the hyperbola, which is on the unshown other half of the double cone. A conic is the curve obtained as the intersection of a plane, called the cutting plane, with the surface of a double cone (a cone with two nappes). It is usually assumed that the cone is a right circular cone for the purpose of easy description, but this is not required; any double cone with some circular cross-section will suffice.
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Tour EDF's most striking characteristic consists in the extrusion of a conic section of the tower on its northern edge. The resulting conic hole extends from the ground floor to the 26th floor and serves as the main entrance to the tower, an entrance built under a wide circular canopy 24 m (79 feet) in diameter. As a consequence, the length of the tower is slightly less at its base than at its top. The cladding of the tower alternates horizontal stripes of plain steel and tinted windows.
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A conic in the projective plane is a curve C that has the following property: If P is a point not on C, and if a variable line through P meets C at points A and B, then the variable harmonic conjugate of P with respect to A and B traces out a line. The point P is called the pole of that line of harmonic conjugates, and this line is called the polar line of P with respect to the conic. See the article Pole and polar for more details.
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Line p is the polar line to point P, l to L and m to M p is the polar line to point P ; m is the polar line to M The concepts of pole, polar and reciprocation can be generalized from circles to other conic sections which are the ellipse, hyperbola and parabola. This generalization is possible because conic sections result from a reciprocation of a circle in another circle, and the properties involved, such as incidence and the cross-ratio, are preserved under all projective transformations.
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It is zero if the conic section degenerates into two lines, a double line or a single point. The second discriminant, which is the only one that is considered in many elementary textbooks, is the discriminant of the homogeneous part of degree two of the equation. It is equal to :b^2 - ac, and determines the shape of the conic section. If this discriminant is negative, the curve either has no real points, or is an ellipse or a circle, or, if degenerated, is reduced to a single point.
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The argument is also spelled out by Bruce Pourciau in "From centripetal forces to conic orbits: a path through the early sections of Newton's Principia", Studies in the History and Philosophy of Science, 38 (2007), pp.56–83.
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Apollonius, Conics, Book I, Definition 4. Refer also to If the figure of the conic section is cut by a grid of parallel lines, the diameter bisects all the line segments included between the branches of the figure.
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The height of the shell attains 6.5 mm, its diameter 8.5 mm. The shell has a depressed-conic shape with a flattened base. It is olive-green, the apex green. The shell is ornamented with deep brown granules.
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A simple oval in the real plane can be constructed by glueing together two suitable halves of different ellipses, such that the result is not a conic. Even in the finite case there exist ovals (see quadratic set).
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Capsule 9-15 x 8-10 mm, ovoid to narrowly ovoid-conic, turning > bright red during maturation. Seeds dark orange-brown to reddish-brown, 1-1.1 mm long, narrowly cylindric, narrowly carinate with terminal expansion, shallowly linear-foveolate.
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The length of the shell varies between 22 mm and 80 mm. The solid, imperforate shell has an ovate-pointed shape. Its color pattern is whitish, or greenish, maculated with brown and olive. The conic spire is acute.
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The size of the shell varies between 35 mm and 60 mm. The imperforate shell has a low-conic shape. Its color pattern is, metallic brownish-purple above, nearly white below. The six whorls are slightly convex above.
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Křovák's projection is conic projection invented by Czech geodesist Josef Křovák. The projection is based on Bessel ellipsoid and it was made for the best projection of Czechoslovakia. It is used for State maps of the Czech Republic.
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The shell grows to a length of 15 mm. The globose- conic shell is narrowly perforate, solid, and light cinereous. It is longitudinally marked with numerous narrow regularly spaced olive lines. The first whorls are bright orange colored.
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The length of the shell varies between 12 mm and 18 mm. The perforate shell has a turreted-conic shape. It is, green, painted with undulating white bands, varied with buff angular lines. The plane whorls are subimbricating.
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The size of the shell varies between 25 mm and 70 mm. The solid, imperforate shell has a conic shape. It is brown or cinereous. The suture is canaliculate, bordered below by a series of curved radiating tubercles.
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The dextral shell is ovate-oblong, spiro-conic, solid, striatulate. The shell is more obsolete toward the apex and with slightly convex whorls. The shell has six whorls. Shell colors are glossy white ornamented with varying brown bands.
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The calculator also has a special section for advanced conic section graphing. Dynamic graphing provides all the functionality of regular graphing, but allows the binding of a variable in the graph equation to time over a value range.
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Hirsch extends this argument to any surface of revolution generated by a conic, and shows that intersection with a bitangent plane must produce two conics of the same type as the generator when the intersection curve is real.
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The size of the shell varies between 60 mm and 90 mm. The imperforate, turbinate-conic shell is, flattened below, imperforate. It is purple rose colored. It is marked with indistinct and very oblique striations above, below white.
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The size of the shell varies between 4 mm and 7.5 mm. The thin, minute shell has a low ovate-conic shape and is amply umbilicated. Its color is ashy white, pearly beneath. The six whorls are convex.
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The size of the shell varies between 35 mm and 45 mm. The turbinate-conic shell has an umbilicus covered by callus. The spire is elevated. Its color pattern is flesh-colored, gold-tinted, and punctate with reddish.
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The milk-white shell has an elongate-conic shape. Its length measures 6 mm. (The whorls of the protoconch are decollated). The nine whorls of the teleoconch are well rounded, slightly excurved at the summit, and weakly shouldered.
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The white shell is ovate, conic, subvitreous, and shining. It measures 2.2 mm. The 1½ whorls of the protoconch are obliquely immersed in the first of the succeeding turns. The 4½ whorls of the teleoconch are well rounded.
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In mathematics, a quadratic set is a set of points in a projective space that bears the same essential incidence properties as a quadric (conic section in a projective plane, sphere or cone or hyperboloid in a projective space).
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The height of the shell varies between 12 mm and 18 mm. The umbilicate shell has a conical shape. It is dull grayish, olivaceous or pinkish, longitudinally lineolate with a darker shade, frequently appearing unicolored. The spire is conic.
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The shell has an elongate-conic shape. The axial sculpture consists of obsolete ribs, frequently only shown in the early turns of the teleoconch. Spiral sculpture, if present, consists of microscopic striations only.G.W. Tryon (1886), Manual of Conchology vol.
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The spire is conic, its outlines straight. The sutures are scarcely visible except for a slightly wider cingulus above them. The whorls number about 6. They are flat, the last angular, nearly flat beneath, shortly deflexed at the aperture.
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Using the same notation as above; If a variable line through the point is a secant of the conic , the harmonic conjugates of with respect to the two points of on the secant all lie on the polar of .
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Part of a parabola (blue), with various features (other colours). The complete parabola has no endpoints. In this orientation, it extends infinitely to the left, right, and upward. The parabola is a member of the family of conic sections.
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The size of the shell varies between 4 mm and 10 mm. The small, solid, umbilicated shell has a depressed-turbinate shape. It is polished, pinkish-white, with oblique, undulating grayish-pink longitudinal stripes. The low spire is conic.
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The size of the shell varies between 18 mm and 40 mm. The solid, false-umbilicate shell has an elate-conic shape. The spire has nearly rectilinear outlines. The about 9 whorls are planulate, the body whorl is carinated.
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The spire is conic, with nearly straight outlines. The sutures are impressed. The spire contains 7-8 whorls, with the last obtusely angular, flat beneath and impressed around the axis. The oblique aperture is rhombic, iridescent and sulcated inside.
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The size of the shell varies between 18 mm and 20 mm. The large, very solid shell is deeply and rather widely false-umbilicate. It has a globose-conic shape. The spire is obtuse and contains about six whorls.
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The height of the shell attains 12 mm. The small, solid, imperforate, whitish shell has an ovate-conic shape. The whorls are a little convex, subimbricating, and separated by profoundly canaliculate sutures;. They are finely crenulated below the sutures.
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The length of the shell attains 12.4 mm, its diameter 4 mm. (Original description) The slender shell has an elongate-conic shape. It is white with narrow brown bands. The type specimen contains 9 whorls forming an elevated spire.
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The solid, subventricose, imperforate shell has an ovate conic shape. Its color pattern is yellowish, longitudinally flammulated. The acute spire is elevated. The convex whorls are sloping above, minutely obliquely striate, encircled by wide flattened ribs, alternating with smaller.
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The wax-yellow shell has an elongate, conic shape. It measures 9 mm. (The nuclear whorls are decollated). The 4½ post-nuclear whorls are moderately well rounded, slightly constricted at the sutures and feebly roundly shouldered at the summit.
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Brianchon's theorem In geometry, Brianchon's theorem is a theorem stating that when a hexagon is circumscribed around a conic section, its principal diagonals (those connecting opposite vertices) meet in a single point. It is named after Charles Julien Brianchon (1783–1864).
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The white shell has a tapering, elongate-conic shape. Its length measures 8.2 mm. The whorls of the protoconch are decollated. The 13 whorls of the teleoconch are flattened, slightly shouldered, and ornamented by strong, rather narrow, oblique, axial ribs.
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The length of the shell attains 8 mm, its diameter 2.5 mm. (Original description by Bartsch) The shell is elongate-conic, white or cream- yellow. The protoconch contains 2½ whorls, well rounded and smooth. The 5 teleoconch whorls are strongly rounded.
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The height of the shell attains 7 mm, its diameter 7½ mm. The rather thin shell is narrowly perforated and has a trochiform shape. The white surface is very shining with nacreous reflections. The conic spire occupies half of the length.
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Reye worked on conic sections, quadrics and projective geometry. Reye's work on linear manifolds of projective plane pencils and of bundles on spheres influenced later work by Corrado Segre on manifolds. He introduced Reye congruences, the earliest examples of Enriques surfaces.
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The shell has an ovate-conic or pyramidal shape. It is imperforate, smooth or spirally sculptured outside, brilliantly iridescent within. The colors are generally bright and variegated. The aperture is less than half the length of shell, longer than wide, ovate.
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The church weathered the Second World War with little damage. But the high conic spire of the tower had been shortened after considerable damage. The remaining stump consists of the massive brick stone construction of the lower parts of the tower.
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The small, buffish shell has an orbiculate-conic shape. It is ornamented with transverse spinulose cinguli (4 on the body whorl). The interstices are clathrate, beautifully dotted with red. This species is readily recognized by its peculiar painting and remarkable sculpture.
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The height of an adult shell attains 35 mm, its diameter 40 mm. The thick, umbilicate shell has a conic-pyramidal shape. It is radiate with white and rose color. it contains 9 whorls, the embryonic smooth, the following planulate.
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The size of the shell varies between 13 mm and 34 mm. The solid, heavy shell has a pyramidal-conic shape. It has a narrowly perforate funnel-shaped umbilicus. Its color is chestnut-brown, purple-brown on the upper whorls.
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The length of the shell varies between 35 mm and 110 mm. The large, solid, umbilicate shell has an orbiculate, conic shape. It is whitish, mottled and strigate with dark brown. This species varies much in degree of elevation and carination.
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The imperforate shell is wheel- shaped. It is low-conic and granulose above, convex below. The periphery is armed with long slender radiating spines, which are concealed at the sutures. The operculum is flat, with a subobsolete arcuate rib outside.
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The style is short, and conic in shape. The pedicel is 2-3mm long. The fruit is coloured glossy green at maturity, with white spots. It is roundish, or slightly longer than broad, or the opposite, and long, by in width.
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The size of the shell varies between 8 mm and 13 mm. The shell is perforate and depressed. It is pinkish-brown, and sparsely black-dotted. The spire has a low-conic shape with an acute apex and five whorls.
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The conic spire is straight sided. The acute apex is white or buf. The sutures are linear, becoming a trifle impressed around the body whorl. The about 7 whorls are planulate, densely spirally striate, the striae stronger on the base.
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The length of the shell varies between 6 and 10 mm. The small, polished shell has a conic shape with pale flesh color. It consists of six whorls, including a minute subglobular nucleus. The suture is distinct but not appressed.
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The shell has a regularly, broadly conic shape. Its length measures 5.4 mm. It is white on the posterior half and light brown on the anterior half of the exposed portion of the whorl. The base of the shell is white.
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The geyser has multiple conic openings sitting on a mound: the cones are about , and the entire mound is tall. The Fly Geyser is the result of man-made drilling in 1916 when water well drilling accidentally penetrated a geothermal source.
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The shell has an elongate-conic shape. Its length measures 3.3 mm. Its color is milk-white, with a narrow, faint yellow band in the middle of the whorls between the sutures. There are ar least two whorls in the protoconch.
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The dextral or sinistral shell is ovate-conic, and colored glossy yellow, green, olive or chestnut; often banded with green or chestnut. The shell has 6 whorls. The color pattern is extremely variable. The height of the shell is 19.0 mm.
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The height of the globose-depressed shell attains 7 mm. Its color is yellowish-white, with purple-brown dots on the spiral ribs. The conic spire is very short and imperforate. The 4½ or 5 whorls increase very rapidlyin size.
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The rather stout, milky white shell is subturrited and has a broadly elongate-conic shape. The length of the shell is 7 mm. The whorls of the protoconch are small. They are almost completely immersed in the first succeeding whorl.
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The broadly conic shell is light green. Its length is 4.4 mm. The nuclear whorls are small and deeply obliquely immersed in the first of the succeeding turns. The six post-nuclear whorls somewhat inflatedly rounded, with well-rounded summits.
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The creamy-white shell is very broadly elongate-conic. It measures 3.3 mm. The nuclear whorls are obliquely immersed in the first of the succeeding turns. The five post-nuclear whorls are moderately well rounded, slightly shouldered at the summit.
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The size of the shell varies between 17 mm and 50 mm. The imperforate, solid shell has a conic shape. It is, white or grayish, mottled and maculated with green, brown or olive. The base of the shell is unicolored, white.
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The length of the shell varies between 30 mm and 75 mm. The imperforate shell has a conic shape. It is greenish, brown maculated. The seven whorls are subplanate, obliquely costulate below the sutures, then with two beaded spiral lirae.
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The bluish-white shell has a conic shape with straight sides. Its length measures 4 mm. The whorls of the protoconch have a depressed helicoid shape. There are six to seven whorls in the teleoconch showing an almost smooth sculpture.
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The shell has an elongate-conic shape, slightly striated. The many whorls of the teleoconch are usually inflated and regularly increasing. They are longitudinally ribbed or smooth. The semioval aperture is entire, widened at its base and rounded in front. .
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The shell is perforate, ovate-conic, very thin, pellucid, scarcely shining, obsoletely and closely decussated by growth striae and delicate spiral lines. The shell is pale corneous in color, sometimes fulvous. The spire is conoid. The apex is rather acute.
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Next, in 1849, Kirkman studied the Pascal lines determined by the intersection points of opposite sides of a hexagon inscribed within a conic section. Any six points on a conic may be joined into a hexagon in 60 different ways, forming 60 different Pascal lines. Extending previous work of Steiner, Kirkman showed that these lines intersect in triples to form 60 points (now known as the Kirkman points), so that each line contains three of the points and each point lies on three of the lines. That is, these lines and points form a projective configuration of type 603603.
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The gills are squarely attached to the stem, and flushed with pink in maturity. The cap of the M. polygramma fruit body is in diameter, and initially egg- to cone-shaped, but expands to become conic to bell-shaped or nearly convex with an abrupt small umbo, or at times plane with a conic umbo. On young fruit bodies, the cap margin is slightly curved inward, and frequently has scalloped edges; in maturity the margin flares out, or is recurved and wavy. The surface of the cap is initially covered with short, fine whitish or grayish hairs that often persist until near maturity.
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There are a lot of Laguerre planes that are not miquelian (see weblink below). The class that is most similar to miquelian Laguerre planes are the ovoidal Laguerre planes. An ovoidal Laguerre plane is the geometry of the plane sections of a cylinder that is constructed by using an oval instead of a non degenerate conic. An oval is a quadratic set and bears the same geometric properties as a non degenerate conic in a projective plane: 1) a line intersects an oval in zero, one, or two points and 2) at any point there is a unique tangent.
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A (non-degenerate) conic is completely determined by five points in general position (no three collinear) in a plane and the system of conics which pass through a fixed set of four points (again in a plane and no three collinear) is called a pencil of conics.. The four common points are called the base points of the pencil. Through any point other than a base point, there passes a single conic of the pencil. This concept generalizes a pencil of circles.Berger, M., Geometry Revealed: A Jacob's Ladder to Modern Higher Geometry (Berlin/Heidelberg: Springer, 2010), p. 127.
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Cavalieri's first book, first published in 1632 and reprinted once in 1650, was , or The Burning Mirror, or a Treatise on Conic Sections.Lo Specchio Ustorio, overo, Trattato delle settioni coniche The aim of Lo Specchio Ustorio was to address the question of how Archimedes could have used mirrors to burn the Roman fleet as they approached Syracuse, a question still in debate. The book went beyond this purpose and also explored conic sections, reflections of light, and the properties of parabolas. In this book he developed the theory of mirrors shaped into parabolas, hyperbolas, and ellipses, and various combinations of these mirrors.
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This conic section is the intersection of the cone of light rays with the flat surface. This cone and its conic section change with the seasons, as the Sun's declination changes; hence, sundials that follow the motion of such light- spots or shadow-tips often have different hour-lines for different times of the year. This is seen in shepherd's dials, sundial rings, and vertical gnomons such as obelisks. Alternatively, sundials may change the angle or position (or both) of the gnomon relative to the hour lines, as in the analemmatic dial or the Lambert dial.
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This does depend on having a K-rational point, which serves as the point at infinity in Weierstrass form. There are many cubic curves that have no such point, for example when K is the rational number field. The singular points of an irreducible plane cubic curve are quite limited: one double point, or one cusp. A reducible plane cubic curve is either a conic and a line or three lines, and accordingly have two double points or a tacnode (if a conic and a line), or up to three double points or a single triple point (concurrent lines) if three lines.
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A Lambert conformal conic projection (LCC) is a conic map projection used for aeronautical charts, portions of the State Plane Coordinate System, and many national and regional mapping systems. It is one of seven projections introduced by Johann Heinrich Lambert in his 1772 publication Anmerkungen und Zusätze zur Entwerfung der Land- und Himmelscharten (Notes and Comments on the Composition of Terrestrial and Celestial Maps). Conceptually, the projection seats a cone over the sphere of the Earth and projects the surface conformally onto the cone. The cone is unrolled, and the parallel that was touching the sphere is assigned unit scale.
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Equivalence of a quadratic Bézier curve and a parabolic segment A quadratic Bézier curve is also a segment of a parabola. As a parabola is a conic section, some sources refer to quadratic Béziers as "conic arcs". With reference to the figure on the right, the important features of the parabola can be derived as follows: # Tangents to the parabola at the end-points of the curve (A and B) intersect at its control point (C). # If D is the midpoint of AB, the tangent to the curve which is perpendicular to CD (dashed cyan line) defines its vertex (V).
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In analogy with the conic sections, the set of points whose Cartesian coordinates satisfy the general equation of the second degree, namely, :Ax^2 + By^2 + Cz^2 + Fxy + Gyz + Hxz + Jx + Ky + Lz + M = 0, where and are real numbers and not all of and are zero, is called a quadric surface. There are six types of non-degenerate quadric surfaces: # Ellipsoid # Hyperboloid of one sheet # Hyperboloid of two sheets # Elliptic cone # Elliptic paraboloid # Hyperbolic paraboloid The degenerate quadric surfaces are the empty set, a single point, a single line, a single plane, a pair of planes or a quadratic cylinder (a surface consisting of a non-degenerate conic section in a plane and all the lines of through that conic that are normal to ). Elliptic cones are sometimes considered to be degenerate quadric surfaces as well. Both the hyperboloid of one sheet and the hyperbolic paraboloid are ruled surfaces, meaning that they can be made up from a family of straight lines.
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They are memorials to the feats of the deceased, every balbal represents an enemy killed by him. Many tombs have no balbals. Apparently, there are buried ashes of women and children. Balbals have two clearly distinct forms: conic and flat, with shaved top.
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The length of the shell attains 6.5 mm, its diameter 3 mm. (Original description) The small shell is rather solid and has an ovate-conic shape. Its Colour is uniform buff. The shell contains six whorls, of which two compose the protoconch.
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He is buried with his wife Pearl, who died on August 13, 1972, at Evergreen Cemetery, Los Angeles. He was succeeded by Bishop Major Rudd Conic who in 1967 relocated Christ Temple Church to its current location on 54th and 10th Ave.
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The yellow shell has a conic shape. Its length measures 5.6 mm. The whorls of the protoconch are decollated. The nine whorls of the teleoconch are appressed at the summit, flattened in the middle, except the last, which is inflated and strongly rounded.
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The large, milk-white, shining shell has an elongate-conic shape. The length of the shell measures 8.4 mm. The whorls of the protoconch are decollated. The 12 whorls of the teleoconch are decidedly rounded, slightly shouldered and somewhat constricted at the periphery.
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The length of the shell attains 5.5 mm, its diameter 2 mm. (Original description) The shell is very small. Its color is white with a brown spot in the middle of the lip varix. The spire is terraced, the lower half conic.
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"conic amusement park recreated in mural". Milford-Orange Bulletin. Many artifacts from the amusement park are preserved in the Savin Rock Museum and Learning Center in West Haven."BEACH: Keeping memories of Savin Rock's glory days alive, one tour at a time".
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A toric section is an intersection of a plane with a torus, just as a conic section is the intersection of a plane with a cone. Special cases have been known since antiquity, and the general case was studied by Jean Gaston Darboux..
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The very heavy, thick, solid shell has a turbinate-conic shape. The shell is smooth or spirally ridged. The outer lip is plicate within. The short, porcellanous columella is strong, cylindrical, bulging or more or less toothed near or at the base.
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The angular periphery is formed of a double beaded ridge, and on some specimens this projects a little at the sutures of the spire. The spire is conic, elevated, with straight lateral outlines. The shell contains nine whorls. The smooth apex is subacute.
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The size of the shell varies between 6 mm and 11 mm. The oval, elongated shell is rather thin, and shining. The elevated spire has a conic shape. It is composed of 4–5 somewhat convex whorls, separated by slightly impressed sutures.
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The short spire is conic. The apical whorl is smooth, the following whorl has three granose lirae, the next with 3 or 4; the penultimate has 7 or 8 equal, grained lirae. The interstices are narrow. The body whorl has ten such lirae.
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The size of the shell varies between 10 mm and 20 mm. The globose-conic shell is more or less depressed. It is imperforate or very narrowly perforate. The sculpture is spirally finely striate, the striae becoming obsolete on the body whorl.
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The base of the shell is tessellated with yellowish and brown. The epidermis is very thin, the pearly inner layer shining partly through it. The spire is conic with its height greater than that of the aperture. The sides are very slightly convex.
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In geometry, two diameters of a conic section are said to be conjugate if each chord parallel to one diameter is bisected by the other diameter. For example, two diameters of a circle are conjugate if and only if they are perpendicular.
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In geometry, Hesse's theorem, named for Otto Hesse, states that if two pairs of opposite vertices of a quadrilateral are conjugate with respect to some conic, then so is the third pair. A quadrilateral with this property is called a Hesse quadrilateral.
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The size of the shell varies between 3 mm and 10 mm. The small, solid, elevated shell has an ovate-conic shape. It is white, with a series of about 10 rufous spots near the suture. The five whorls form a conical spire.
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The length of the shell varies between 10 mm and 22 mm. The imperforate shell has a globose-turbinate shape. Its color pattern is pale fleshy, vividly painted with reddish brown. The conic spire contains five convex whorls with narrowly channelled sutures.
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The very elongate-conic, heavy shell is very light yellow. The shell measures 9.5 mm. The nuclear whorls are small, almost completely obliquely immersed in the first of the succeeding turns. The 6 ½ post-nuclear whorls are situated rather high between the sutures.
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The conic shell is crystalline, and shining. It measures 3.6 mm. The whorls of the protoconch number one and one-half, and are the greater part immersed in the first of the succeeding turns. The five whorls of the teleoconch are flattened.
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The size of the shell varies between 20 mm and 60 mm. The imperforate, solid, heavy shell has a turreted-conic shape. It is flesh- colored, lighter beneath. It contains about 12 whorls, somewhat convex toward the lower, concave toward the upper part.
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The height of the shell attains 15 mm, its diameter 20 mm. The umbilicate shell has a globose-conic shape. The 6 to 7 whorls are encircled by numerous unequal, grained, partly pearly riblets. The convex base is sculptured with smoother riblets, their interstices cancellated.
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The shell attains a length of 25 mm, its diameter 9 mm. (Original description) The large, rather thin shell is elongate conic. The earlier whorls are angled, the last rounded. The colour of the shell is cream wiih a few irregularly scattered pale brown spots.
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All other polycons' edges are hyperbolic. Like the polycons, the Platonicons are made of only one type of conic surface. Their unique feature is that each one of them circumscribes one of the five Platonic solids. Unlike the other families, this family is not infinite.
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The milk-white shell has an elongate-conic shape. Its length measures 4 mm. The whorls of the protoconch number more than one. They are obliquely immersed in the first of the succeeding turns, above which the tilted edge of the last volution only projects.
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It usually has a rounded conic form, that becomes irregular with age. The tree can be long-lived, with some trees over 500 years old. It needs full sun to grow well, is intolerant of shade, and is resistant to snow and ice damage.
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The slender shell is elongate, conic, milk-white. It measures 3 mm. The three nuclear whorls are moderately large, helicoid. They have their axis at a right angle to the axis of the later whorls and are scarcely immersed in the first of them.
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The shell is thin, narrowly umbilicate, conic, shaped like Lyogyrus brownii Carpenter. The color of the shell is slightly yellowish corneous. The shell is thin, smooth, with faint growth-lines. The shell has 4 whorls that are very convex and separated by deeply constricting sutures.
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The height of the shell is up to 60 mm, and the width is up to 120 mm. The large shell has a depressed-conic shape. Below widely it is umbilicate and concave. The spire is dome-shaped, and consists of 5 convex whorls.
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Pupoid protoconch (enlarged) of Nisiturris crystallina The very slender and thin, almost transparent shell has an elongate-conic shape. Its length varies between 2.9 mm and 4.5 mm. It is slightly umbilicated. The smooth whorls of the protoconch are large, and very much elevated.
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The spire is conic, scalar and somewhat higher than the aperture. The protoconch is smooth, with a flatly rounded nucleus. The shell contains 8 whorls, the earlier ones flattish, the others convex, with a narrow shoulder or depression. The base of the shell is contracted.
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The size of the shell varies between 15 mm and 30 mm. The thick, solid, imperforate shell has a depressed conical shape. It is blackish, dotted upon the ribs with yellow or white. The conic spire is more or less depressed with an acute apex.
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The minute, white shell has a conic shape. The length is 0.65 mm. The protoconch is mammillated. The whorls of the teleoconch are marked by five spiral lirations of which two appear between the sutures, one at the periphery and two on the base.
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The shell is small, cylindric, terminating above in a conic spire, retaining all the whorls, rimate or perforate. The shell has 11-21 whorls, which are closely coiled. The first 1½ of whorls are smooth. The rest of whorls are smooth, striate or ribbed.
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FA is a measure often used in diffusion imaging where it is thought to reflect fiber density, axonal diameter, and myelination in white matter. The FA is an extension of the concept of eccentricity of conic sections in 3 dimensions, normalized to the unit range.
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The height of the shell varies between 35 mm and 40 mm, its diameter between 45 mm and 47 mm. The false-umbilicate shell has a regularly conic shape. It is concave below. Its color is greenish and roseus, under a dull grayish-green cuticle.
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These markings are often interrupted into spiral series of articulations. The epidermis is thin, shining, and easily rubbed off. The spire is elevated conic. Its sides are straight or slightly concave, more or less eroded, and showing the iridescent green nacre at the tip.
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The length of the shell varies between 50 mm and 120 mm. The large, solid shell has a globose-conic shape. It is ventricose and imperforate. Its color is green, irregularly mottled and spirally striped with chestnut, closely irregularly striate with the same color.
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The shell grows to a length of 75 mm. The solid, imperforate shell has an ovate- conic shape. Its color pattern is dirty white or greenish, maculate or tessellate with dark. The six whorls are convex, rounded, more or less angular around the upper part.
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The length of the shell varies between 10 mm and 35 mm. The acute, elongate, imperforate shell has an ovate-conic shape. The six whorls are rounded, transversely lirate, radiate and finely striate. The body whorlscarcely exceeds the balance of the shell in length.
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The length of the shell varies between 75 mm and 240 mm. The large, solid, imperforate shell has an ovate-conic shape with an acute spire. The color of its epidermis is castaneous or olive. The eight whorls are rounded and increase regularly in size.
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The size of the shell varies between 13 mm and 25 mm. The solid but rather thin, imperforate, shell has a conic-elevated shape. It is greenish olive, with narrow irregular longitudinal blackish-olive stripes. The seven strongly convex whorls have a rounded form.
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The size of the shell varies between 12 mm and 26 mm. The solid, imperforate shell has a conical shape. It is pinkish with darker flames above alternating with short white stripes or spots radiating from the sutures. The spire is rather straight conic.
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The solid, imperforate shell has a conic shape. Its color pattern is soiled white, more or less tinged with green and brown. The elevated spire has an acute apex. The 6-7 whorls are convex, with fine incremental striae and oblique radiating folds above.
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The height of the shell varies between 45 mm and 70 mm, its diameter between 45 mm and 60 mm. The solid, thick shell has a conic-pyramidal shape. Its, axis is imperforate but appears sub-umbilicate. It is white, longitudinally flammulated with bright red.
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The height of the shell attains 45 mm, its diameter 40 mm. The solid, imperforate shell has a conic-pyramidal shape. It is white, above longitudinally broadly flammulated with red. The spire is somewhat attenuated and concave on its upper portion, then slightly convex.
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This discussion started from the definition of a parabola as a conic section, but it has now led to a description as a graph of a quadratic function. This shows that these two descriptions are equivalent. They both define curves of exactly the same shape.
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Morton, Pierce. Geometry, Plane, Solid, and Spherical, in Six Books, page 228 (Baldwin and Cradock, 1830). Liber (book) II, Propositio (proposition) XXXVII (37). The focus-directrix property can be used to give a simple proof that astronomical objects move along conic sections around the Sun.
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The shell has an elongate-conic shape. It is white on the shoulder, the rest light brown. Its length measures 5.3 mm. (The whorls of the protoconch are decollated.) The ten whorls of the teleoconch are flattened in the middle, well contracted at the sutures.
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The size of the shell varies between 10 mm and 18 mm, the diameter is up to 13 mm. The narrowly perforate shell has a conic-acute shape. The 9 to 10 whorls are planulate. The embryonic whorls are smooth, buff, the remaining whitish-buff.
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The length of the shell attains 4.5 mm, its diameter 2 mm. The small, solid shell has a cylindro-conic shape. Its colour is ferruginous, with an ochraceous orange band on the shoulder. Another specimen is uniform orange, except the varix, which is ferruginous.
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The shell has an elongate-conic shape. Its length measures 6.2 mm. The two helicoid whorls of the protoconch are depressed. Their axis is at nearly right angles to that of the succeeding turns, in the first of which they are very slightly immersed.
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The shell has an elongate-conic shape. Its length measures 9.5 mm. Its color is wax yellow with a broad subsutural, narrow submedian and a broad subperipheral band of golden brown. These color markings make this species different from Turbonilla lituyana and Turbonilla oregonensis.
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The slender shell has an elongate-conic shape. Its posterior half between the sutures is light yellow; the anterior half of the base is chestnut. The length of the shell measures 4.8 mm. The two whorls of the protoconch form a depressed, helicoid spire.
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The dextral shell is elongate-conic, imperforate with convex whorls and a slightly impressed line below the suture. The shell has five whorls. The color is green with light streaks intermixed. The aperture is subovate and stained with a pink color just within the margin.
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The thin, semitranslucent, bluish white shell has an elongate-conic shape. Its length measures 4.9 mm. The whorls in the protoconch number at least two. They are rather large, depressed helicoid, well rounded, and about half immersed in the first of the succeeding turns.
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The spire is conic, turreted, of the same height as the aperture. The protoconch consists of about 2 whorls. The nucleus is smooth, convex, slightly lateral,the second whorl convex, and minutely reticulated. The 6½ subsequent whorls are distinctly shouldered, flatly rounded below the angle.
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The Kiepert hyperbola is the unique conic which passes through the triangle's three vertices, its centroid, and its circumcenter. Of all triangles contained in a given convex polygon, there exists a triangle with maximal area whose vertices are all vertices of the given polygon.
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The shell is very elongate-conic, yellowish-white. It measures 5.6 mm. The small nuclear whorls are immersed in the first of the succeeding turns, above which only half of the last volution projects. The seven post-nuclear whorls are situated high between the sutures.
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Cultivars include 'Nova', 'Duros' (with an upright crown), the pyramidal 'Frontyard' and the conic-crowned 'Redmond'. The tree was introduced to the UK in 1752, but has never prospered there, being prone to dieback.Bean, W. J. (1921). Trees and shrubs hardy in the British Isles.
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The third chapter brings in more modern concepts of algebraic geometry including the degree and genus of an algebraic curve, and rational mappings and birational equivalences between curves. Chapters four and five concern conic sections, and the theorem that when a conic has at least one rational point it has infinitely many. Chapter six covers the use of secant lines to generate infinitely many points on a cubic plane curve, considered in modern mathematics as an example of the group law of elliptic curves. Chapter seven concerns Fermat's theorem on sums of two squares, and the possibility that Diophantus may have known of some form of this theorem.
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A conic in a projective plane that contains the two absolute points is called a circle. Since five points determine a conic, a circle (which may be degenerate) is determined by three points. To obtain the extended Euclidean plane, the absolute line is chosen to be the line at infinity of the Euclidean plane and the absolute points are two special points on that line called the circular points at infinity. Lines containing two points with real coordinates do not pass through the circular points at infinity, so in the Euclidean plane a circle, under this definition, is determined by three points that are not collinear.
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The Veronese surface arises naturally in the study of conics. A conic is a degree 2 plane curve, thus defined by an equation: :Ax^2 + Bxy + Cy^2 +Dxz + Eyz + Fz^2 = 0. The pairing between coefficients (A, B, C, D, E, F) and variables (x,y,z) is linear in coefficients and quadratic in the variables; the Veronese map makes it linear in the coefficients and linear in the monomials. Thus for a fixed point [x:y:z], the condition that a conic contains the point is a linear equation in the coefficients, which formalizes the statement that "passing through a point imposes a linear condition on conics".
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An elliptic, parabolic, and hyperbolic Kepler orbit: Elliptic orbit by eccentricity The orbital eccentricity of an astronomical object is a dimensionless parameter that determines the amount by which its orbit around another body deviates from a perfect circle. A value of 0 is a circular orbit, values between 0 and 1 form an elliptic orbit, 1 is a parabolic escape orbit, and greater than 1 is a hyperbola. The term derives its name from the parameters of conic sections, as every Kepler orbit is a conic section. It is normally used for the isolated two-body problem, but extensions exist for objects following a Klemperer rosette orbit through the galaxy.
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A parabola can be considered as the affine part of a non-degenerated projective conic with a point Y_\infty on the line of infinity g_\infty, which is the tangent at Y_\infty. The 5-, 4- and 3- point degenerations of Pascal's theorem are properties of a conic dealing with at least one tangent. If one considers this tangent as the line at infinity and its point of contact as the point at infinity of the y axis, one obtains three statements for a parabola. The following properties of a parabola deal only with terms connect, intersect, parallel, which are invariants of similarities.
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Like the other 13 species members of its genus, Eriophyllum latilobum presents generally alternate leaves ranging from entire to nearly compound. The flower heads are grouped in radiate, flat-topped heads, with an hemispheric to nearly conic involucre. Phyllaries are either free, or more or less fused, their receptacle flat, but naked and conic in the center. The ray flowers (the "petals") have yellow ligules entire to lobed. Fruits are 4-angled cylindric achenes in the outer flowers, but are generally club-shaped for the inner flowers; the pappus is somewhat jagged.Mooring, Madroño 38:213–226, (1991) Eriophyllum latilobum occurs as a subshrub between 20 and 50 centimeters in height.
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One of the contributions of Terzioglu as the director of the Mathematics Research Institute to Turkey's mathematical culture and the history of science was the systematic scan of the Islamic literature relevant to mathematics and the presentation of the information related to conic sections in ancient mathematics to the scientific community. As a result of these efforts, the facsimile of two ancient texts of mathematics originally written in Arabic were realized. The first one is the preface of Mecmuatu'r-risail, the Arabic translation by Beni Musa b. Sakir (died in 873) of Conica, which is the work of Apollonius of Perga (BC 262–190) on the conic sections.
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Particularly of interest to Pascal was a work of Desargues on conic sections. Following Desargues' thinking, the 16-year-old Pascal produced, as a means of proof, a short treatise on what was called the "Mystic Hexagram", "Essai pour les coniques" ("Essay on Conics") and sent it—his first serious work of mathematics—to Père Mersenne in Paris; it is known still today as Pascal's theorem. It states that if a hexagon is inscribed in a circle (or conic) then the three intersection points of opposite sides lie on a line (called the Pascal line). Pascal's work was so precocious that Descartes was convinced that Pascal's father had written it.
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Under standard assumptions, a body moving under the influence of a force, directed to a central body, with a magnitude inversely proportional to the square of the distance (such as gravity), has an orbit that is a conic section (i.e. circular orbit, elliptic orbit, parabolic trajectory, hyperbolic trajectory, or radial trajectory) with the central body located at one of the two foci, or the focus (Kepler's first law). If the conic section intersects the central body, then the actual trajectory can only be the part above the surface, but for that part the orbit equation and many related formulas still apply, as long as it is a freefall (situation of weightlessness).
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The change in rock type can be clearly seen at several points around the loch, as it runs across the islands of Inchmurrin, Creinch, Torrinch and Inchcailloch and over the ridge of Conic Hill. To the south lie green fields and cultivated land; to the north, mountains.
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The bluish-white, slender shell has an elongate-conic shape. Its length measures 7.4 mm. The 2½ whorls of the protoconch are small and helicoid. Their axis is at right angles to that of the succeeding turns, in the first of which they are slightly immersed.
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Pascal's theorem (also known as the "Hexagrammum Mysticum Theorem") states that if an arbitrary hexagon is inscribed in any conic section, and pairs of opposite sides are extended until they meet, the three intersection points will lie on a straight line, the "Pascal line" of that configuration.
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The milk-white shell has an elongate-conic shape. Its length measures 6.5 mm. It is umbilicated. The whorls of the protoconch are small, obliquely immersed in the first of the turns of the teleoconch, above which only the tilted edge of the last volution projects.
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The light- brown shell has an elongate-conic shape. The length measures 6.1 mm. The two whorls of the protoconch are small. They are planorboid, having their axis at right angles to that of the succeeding turns, in the first of which they are very slightly immersed.
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P. bryantwalkeri is a small snail that has a height of and globose to ovate-conic shell. Its differentiated from other Pyrgulopsis in that its penial filament has a very weak lobe and short filament with the penial ornament consisting of a weakly developed terminal gland.
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The Lund’s fly is parasitic at its larval stage. Under examination with a scanning electron microscope, it appears whitish and barrel-shaped, with 11 segments. Its body is almost completely covered by large conic-shaped spines. These spines serve as a point of attachment to its host.
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The height of the shell attains 19 mm. The solid, thick shell has a globose-conic shape. it is imperforate when adult, umbilicate in the young,. Its color is whitish or yellowish, marked longitudinally with narrow black stripes, or series of black spots on the spirals.
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The height of the shell attains 9 mm, its diameter also 9 mm. The solid shell is narrowly umbilicate and has a globose-conoida shape. It is whitish, maculated with chestnut, sometimes banded, often punctate and articulated with white dots. The conic spire is acute and short.
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The conic spire is acute. The sutures are subcanaliculate. The five to six whorls are convex, spirally granose-lirate. The body whorl is rounded, encircled by 14 or 15 conspicuously granose equal ridges, the interstices finely obliquely striate, and with more or less obvious spiral striae.
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The seeds are vertical and spherical in shape, light brown, hairy and also have a membrane on the exterior. The hairs take on many forms – they can be angular, slight, curved, conic or straight. There is no feeding tissue (also known as the perisperm) within the seed.
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The length of the shell varies between 25 mm and 80 mm. The solid, perforate shell has an ovate-conic shape. Its color pattern is green or gray, radiately flammulated with black, green or brown, sometimes unicolored. The six whorls are convex and sometimes subangulate above.
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The size of the shell varies between 15 mm and 25 mm. The imperforate shell is pale ashen. It has an elevated-conic shape with an acute apex. The seven whorls are planulate above, with radiating oblique folds, which are produced into short spines at the periphery.
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The acute spire is elevated conical, with sides slightly convex. The protoconch is conic with 1½ strongly convex smooth whorls, which are mostly pearly. The six whorls of the spire are flatly convex, the last angled at the periphery. The base of the shell is slightly convex.
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The white shell has a broadly elongate-conic shape. Its length measures 5 mm. The whorls of the protoconch are well rounded, and smooth. They are obliquely immersed in the first of the succeeding turns, above which the tilted edge of the last volution only projects.
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P. bernardina is a small snail that has a height of and a narrowly conic, small shell. Its differentiated from other Pyrgulopsis in that its penial filament has an absent lobe and elongate filament with the penial ornament consisting of centrally positioned dorsal and ventral glands.
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The bluish-white shell is large and robust and has an elongate-conic shape. Its length measures 15 mm. The whorls of the protoconch are decollated. The nine whorls of the teleoconch are slightly rounded, roundly shouldered at the summit and weakly contracted at the suture.
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In particular, it adds conic sections like circles and ellipses to the set of curves that can be represented exactly. The term rational in NURBS refers to these weights. The control points can have any dimensionality. One- dimensional points just define a scalar function of the parameter.
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The shell is small, measuring 3.1 mm. It is regularly conic, bluish-white. The nuclear whorls are deeply and obliquely immersed in the first of the succeeding turns, above which only the tilted edge of the last volution projects. The 5½ post-nuclear whorls are slightly rounded.
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The size of the shell varies between 25 mm and 75 mm. The imperforate, very solid shell has a turbinate-conic shape. Its color pattern is dirty white or pale green, radiately maculated with brown above, irregularly marked and lighter below. The shell contains six whorls.
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The thin shell has a broadly conic shape. It is semitranslucent, bluish-white. Its length measures 3.3 mm. The whorls of the protoconch are very obliquely immersed in the first of the succeeding turns, above which only the last half of the last turn is visible.
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The white shell has an elongate-conic shape. Its length measures 2.8 mm. The three whorls of the protoconch are smooth and heterostrophic, i. e. coiled in the opposite direction to the whorls of the teleoconch. The teleoconch contains 8 whorls separated by a pronounced suture.
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The crystalline shell has an ovate, conic, shape. Its length measures 2.5 mm. The 1½ whorls of the protoconch are obliquely immersed in the first of the succeeding turns. The four whorls of the teleoconch are strongly constricted at the sutures, and moderately shouldered at the summit.
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The milk-white shell has an elongate-conic shape. Its length measures 4.5 mm. There are at least two whorls in the protoconch. These are smooth, deeply obliquely immersed in the first of the succeeding turns, above which only a portion of the last two turns project.
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The length of the shell attains 23 mm. (Original description) The shell has an elongate-conic shape. It is pale yellow, with a faint brown band encircling the whorls a little anterior to the sinal sulcus at the summit. The protoconch contains 1.5, smooth, well rounded whorls.
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It has an octagonal prismatic form and is covered with a conic stone cupola. This form is odd for monuments of Baku and Absheron. Such kinds of constructions are met beyond Baku and partially in Shamakhi Rayon. The mausoleum is divided into two parts: overground and underground.
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As the dimension of a Euclidean plane is two, quadrics in a Euclidean plane have dimension one and are thus plane curves. They are called conic sections, or conics. Circle (e = 0), ellipse (e = 0.5), parabola (e = 1), and hyperbola (e = 2) with fixed focus F and directrix.
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In any case, the intersection curve of a plane and a quadric (sphere, cylinder, cone,...) is a conic section. For details, see.CDKG: Computerunterstützte Darstellende und Konstruktive Geometrie (TU Darmstadt) (PDF; 3,4 MB), p. 87–124 An important application of plane sections of quadrics is contour lines of quadrics.
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The milk-white shell has an elongate-conic shape. Its length measures 8.3 mm. The two, small whorls of the protoconch are depressed and helicoid. They have their axis at right angles to that of the succeeding turns, in the first of which they are about one-third immersed.
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In 1856, he was appointed professor of mathematics at Halle, and in 1858 at Breslau. Joachimsthal, who was Jewish, contributed essays to Crelle's Journal, 1846, 1850, 1854, 1861, and to Torquem's Nouvelles Annales des Mathématiques. He is known for Joachimsthal's Equation and Joachimsthal Notation , both associated with conic sections.
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The size of the shell varies between 9 mm and 20 mm. The very solid shell has an elate-conic shape. It is narrowly false-umbilicate, red or reddish brown, dotted with black; rosy at the apex. The outlines of the spire are a little concave toward the apex.
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The size of the shell varies between 5 mm and 11 mm. The small shell has a globose-conic shape and is very similar in form to Clanculus corallinus. The five whorls are acutely granose-lirate. They are brown, below the sutures more or less maculated with blackish.
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The spiral riblets are lighter, the apex is dark, usually purple. The surface is encircled by numerous spiral smooth riblets, their interstices closely finely obliquely striate. The riblets usually number 7 to 9 on the penultimate whorl, about 9 on the base. The spire is conic, the apex acute.
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The very small, solid shell is perforate or has a narrow umbilicus. It contains a few convex whorls. The protoconch consists of one or two smooth whorls. The turbinate or globoso-conic shell shows numerous subequal spiral cords with in their intervals well developed or weak cross threads.
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The size of the shell varies between 4 mm and 5.5 mm. The small, solid, thick shell has a globose-conic shape, evenly grained all over. it is blackish or pink varied with darker. It is imperforate when adult, and has a groove at the place of the umbilicus.
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The small, white shell has an ovate-conic shape and is spirally striate. The interstices, with the aid of lens, appear finely striate longitudinally. The shell is ornated around the sutures with bright, rose- colored, equidistant flamules. The five convex whorls, including the apex, are obtuse at the periphery.
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The uniformly pale brown shell is very large (compared with the other species in this genus) and has an elongate conic shape . Its length measures 13.8 mm. The whorls of the protoconch are decollated. The 13 whorls of the teleoconch are well rounded, and strongly appressed at the summit.
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The height of the shell attains 8 mm, its diameter 7.5 mm. The small, imperforate, thick, solid shell has a globose-conic shape. It is blackish, speckled and maculated all over with yellowish. The body whorl is spirally encircled by two narrow bands of black articulated with orange.
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The size of the shell varies between 10 mm and 35 mm. The very thick and solid imperforate shell is subperforate in the young. It has a globose-conic shape. It is dull grayish, densely marked all over with very numerous fine flexuous or zigzag braided purplish-black lines.
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The columellar lip is rounded and broader than the rest.Dall (1919) Descriptions of new species of Mollusca from the North Pacific Ocean; Proceedings of the U.S. National Museum, vol. 56 (1920) (described as Margarites frigidus) The height of the shell attains 9 mm. The small, conic shell is polished.
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The length of the shell varies between 4 mm and 8 mm. The smooth, shining shell has a globose-conic shape. The small shell is composed of four to five convex whorls, the two first very small, convex and depressed; the others very large. The sutures are linear.
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The broadly conic shell is yellowish-white. The 2½ whorls of the protoconch are very small. They form a rather elevated helicoid spire. Its axis is at right angles to that of the succeeding turns, in the first of which it is a little more than half immersed.
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P. bacchus is a small snail that has a height of and an ovate- conic, medium-sized shell. Its differentiated from other Pyrgulopsis in that its penial filament has a short lobe and medium length filament with the penial ornament consisting of a transverse, often fragmented terminal gland.
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The dextral shell is conic and solid. The shell has six whorls. The glossy color is a uniform white, or ivory yellow with a white sutural line or either of these tints with a burnt sienna band immediately above a wider and darker band. The suture is margined.
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The height of the shell attains 3.5 mm, its diameter 5 mm. The shell has a depressed conic shape. The nuclear whorls are white. The postnuclear whorls are marked with broad axial bands of brown which may extend entirely across the whorls, or may be interrupted in the middle.
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Excavated, hollowed out. Conchiolin. Conic. Shaped like a cone. Connective. A part connecting two other parts, as a muscle connecting two parts of the body, or a nerve connecting two ganglia. Constricted. Narrowed. Contractile. Capable of being contracted or drawn in, as the tentacle of a snail. Convex.
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Wallis's conical edge is also a kind of right conoid. Figure 2 shows that the Wallis's conical edge is generated by a moving line. Wallis's conical edge is named after the English mathematician John Wallis, who was one of the first to use Cartesian methods to study conic sections.
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Marstonia comalensis is a species of minute freshwater snail with a gill and an operculum, an aquatic gastropod mollusk or micromollusk in the family Hydrobiidae. It is found in south central Texas, United States. Marstonia comalensis is large for this genus. It has an ovate-conic, openly umbilicate shell.
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In 1710, he moved to London, staying in the house of the father of John Bowes, who had been one of Jollie's students and would one day become Lord Chancellor of Ireland. Whilst here, he studied geometry, conic sections, algebra, French, and John Locke's Essay Concerning Human Understanding.
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The short-conic spire has rectilinear outlines. The about eight whorls are subconcave above, and slightly convex. They contain a subsutural subsquamose carina, and are encircled by numerous subequal granulose lirae. The body whorl is acutely carinated below the middle, slightly excavated above and flat below the carina.
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The rather large shell has an elongate conic shape. Its length measures 12.5 mm. Its color is light brown. The early whorls have a light yellow color.. The whorls of the protoconch are decollated. The 11½ whorls of the teleoconch are appressed at the summit, which is slightly excurved.
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The shell has an elongate-conic shape. It is milk-white, with a broad yellow band a little anterior to the middle of the whorls between the sutures. Its length varies between 3.6 mm and 4.3 mm. The two whorls of the protoconch form a depressed helicoid spire.
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This was given by Isaac Newton through his Inverse Square Law. (Proposition 4), and relationships between centripetal forces varying as the inverse-square of the distance to the center and orbits of conic-section form (Propositions 5–10). Propositions 11–31 establish properties of motion in paths of eccentric conic-section form including ellipses, and their relation with inverse-square central forces directed to a focus, and include Newton's theorem about ovals (lemma 28). Propositions 43–45 are demonstration that in an eccentric orbit under centripetal force where the apse may move, a steady non-moving orientation of the line of apses is an indicator of an inverse- square law of force.
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Parabolic compass designed by Leonardo da Vinci The earliest known work on conic sections was by Menaechmus in the 4th century BC. He discovered a way to solve the problem of doubling the cube using parabolas. (The solution, however, does not meet the requirements of compass-and-straightedge construction.) The area enclosed by a parabola and a line segment, the so-called "parabola segment", was computed by Archimedes by the method of exhaustion in the 3rd century BC, in his The Quadrature of the Parabola. The name "parabola" is due to Apollonius, who discovered many properties of conic sections. It means "application", referring to "application of areas" concept, that has a connection with this curve, as Apollonius had proved.
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A (non- degenerate) conic is completely determined by five points in general position (no three collinear) in a plane and the system of conics which pass through a fixed set of four points (again in a plane and no three collinear) is called a pencil of conics.. The four common points are called the base points of the pencil. Through any point other than a base point, there passes a single conic of the pencil. This concept generalizes a pencil of circles. In a projective plane defined over an algebraically closed field any two conics meet in four points (counted with multiplicity) and so, determine the pencil of conics based on these four points.
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3-tangents degeneration of Brianchon's theorem As for Pascal's theorem there exist degenerations for Brianchon's theorem, too: Let coincide two neighbored tangents. Their point of intersection becomes a point of the conic. In the diagram three pairs of neighbored tangents coincide. This procedure results in a statement on inellipses of triangles.
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The large, bluish-white shell is slender and has an elongate conic shape. Its length measures 9.2 mm. The 2¼ whorls of the protoconch are small, and depressed helicoid. Their axis is at right angles to that of the succeeding turn, in the first of which they are slightly immersed.
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The aperture is fulvous inside. The spire is conic, turriculate, very little higher than the aperture. The protoconch is papillate and consists of two smooth convex whorls. The shell contains 6 whorls, the last high in proportion, with a sloping, broad, and lightly excavated shoulder, slightly convex below the inconspicuous angle.
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The yellowish white shell is slender and has an elongate-conic shape. Its length measures 6.3 mm. The 2½ whorls of the protoconch are small, and depressed helicoid. Their axis is at right angles to that of the succeeding turns, in the first of which they are about one-fourth immersed.
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The bluish-white shell is semi translucent and has an elongate-conic shape. Its length is 4.7 mm. The 2½ whorls of the protoconch form a rather solute, elevated, helicoid spire. Its axis is at right angles to the succeeding turns, in the first of which it is slightly immersed.
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Nowadays the term "Rogallo wing" is synonymous with one composed of two partial conic surfaces with both cones pointing forward. Slow Rogallo wings have wide, shallow cones. Fast subsonic and supersonic Rogallo wings have long, narrow cones. The Rogallo wing is a simple and inexpensive flying wing with remarkable properties.
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The small, milk-white shell grows to a length of 2.0 mm. It is umbilicated, regularly conic with an obliquely truncated apex and deeply channeled sutures. The whorls of the protoconch are almost completely immersed in the first whorl of the teleoconch. Only half of the last volution projects above it.
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P. californiensis is a small snail that has a height of and elongate-conic shell. Its differentiated from other Pyrgulopsis in that its penial filament has an elongate lobe and elongate filament with the penial ornament consisting of an elongate penial gland; large, curved, transverse terminal gland; and several ventral glands.
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The size of the shell varies between 8 mm and 13 mm. The thin, small, umbilicate shell has a conical shape. The coloration is very variable, sometimes uniform dark brown or red, sometimes cinereous, longitudinally clouded with brown, or with spiral series of blackish dots. The low-conic spire is gradate.
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Midway between these are smaller ones, and there are still finer spiral striae occupying the interstices. The whole is decussated by fine striae of growth. There is an angle or carina midway between the periphery and suture of the body whorl, which angulates the spire whorls. The short spire is conic.
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The obtuse spire is dome-shaped, or low-conic and contains five whorls. The upper ones are sometimes angulate, spirally lirate with the lirie wider than their interstices, on the body whorl often subobsolete. The last whorl descends, and is somewhat concave below the suture. The oval aperture is white within.
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The shell attains a height between 50 mm and 60 mm. The perforate, solid shell has an ovate-conic shape. Its color pattern is dirty white or greenish, radiately flammulated above and maculate below with black or brown. The six whorls are convex, slightly flattened below the subcanaliculate sutures, sometimes subcarinate.
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The size of the shell varies between 25 mm and 80 mm. The orbiculate, imperforate shell has a depressed-conic shape. It is, pinkish yellow, unicolored, or clouded with purplish or brown. The seven whorls are rounded, the upper two smooth, the others closely minutely granulose in regular spiral series.
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The acute, conic spire is very short. The sutures are more impressed than usual in this group. The five whorls are quite convex, the upper ones ruddy or purplish, the last very large, slightly compressed just below the suture, and gently descending anteriorly. The very large aperture is very oblique.
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The milk-white shell has an elongate-conic shape. Its length measures 6.7 mm. The 2¼ whorls of the protoconch are small. They form a moderately elevated spire whose axis is at right angles to that of the succeeding turns, in the first of which it is about one-fourth immersed.
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Perithecial stromata which mature in spring are also short conic and 1–2 mm in diameter. The interior tissue is pale yellow to grayish brown with 5-30 black perithecia embedded within. Perithecia are 200-600 µm in diameter, and their necks converge at the disc-like top of the stroma.
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This optimization problem can then be solved by standard optimization methods. Adaptations of existing techniques such as the Sequential Minimal Optimization have also been developed for multiple kernel SVM-based methods.Francis R. Bach, Gert R. G. Lanckriet, and Michael I. Jordan. 2004. Multiple kernel learning, conic duality, and the SMO algorithm.
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An anonymous Geometrical System of Conic Sections, Cambridge, 1822, was ascribed to Marrat in the catalogue of the Liverpool Free Library. He compiled Lunar Tables, Liverpool, 1823, and wrote The Elements of Mechanical Philosophy, 1825. At this period he compiled the Liverpool Tide Table, and was a contributor to Blackwood's Magazine.
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Scientists: Extraordinary People Who Altered the Course of History. New York: Metro Books. g. 12. In the Elements, Euclid deduced the theorems of what is now called Euclidean geometry from a small set of axioms. Euclid also wrote works on perspective, conic sections, spherical geometry, number theory, and mathematical rigour.
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The shell attains a height of 21 mm, its diameter 19 mm. The imperforate, elevated shell has a conic shape with an acute apex. Its color pattern is pale yellowish. The seven whorls are slightly convex, obliquely radiately costate with distant folds, which are prominently nodulose at the sutures and periphery.
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The cap is 2.5–4 cm in diameter, conic to convex, and smooth to slightly striate, sometimes with a small umbo. The cap surface is pale brown to reddish brown in color, hygrophanous, and bruises blue where damaged. Its gills are subadnate, thin, and brown. The stipe is 5 cm by .
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The broadly conic shell is milk-white and measures 3.5 mm. The whorls of the protoconch are deeply obliquely immersed, apparently smooth. The six whorls of the teleoconch are well rounded. They are marked with three strong, equal spiral keels, the posterior two of which are tuberculate, the third one smooth.
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The white shell moderately large measuring 3.2 mm. It is elongate-conic, with decidedly channeled sutures. The nuclear whorls number at least 2, forming a depressed helicoid spire, which is obliquely, almost one- half immersed in the first of the succeeding turns. The six post-nuclear whorls are moderately rounded.
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The milk-white shell has an extremely slender, elongate conic shape. The length of the type specimen measures 5.8 mm. The whorls of the protoconch of the type specimen are decollated and the first three whorls of the teleoconch are probably lost. The remaining 9¼ whorls of the teleoconch are flattened.
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The elongate-conic shell is very regular in outline, yellowish white, shining. Its length measures 4 mm. The whorls of the protoconch are almost completely immersed in the first of the succeeding volution. The whorls of the teleoconch are moderately rounded, rather high between the sutures, slightly shouldered at the summits.
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The firm and narrow sepals are long and the pedicels are long. The capsules vary in shape from lanceolate to slenderly conic, with three carpels and three styles. The capsules are long and thick. The plant flowers from July to September and fruits from early October to the end of autumn.
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The distance from the foot to the center is the radius of curvature. The latter is the radius of a circle, but for other than circular curves, the small arc can be approximated by a circular arc. The curvature of non-circular curves; e.g., the conic sections, must change over the section.
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The stems gradually become deep brown near the base. The cap is light reddish-brown, with a diameter typically ranging from . Initially conic to bell-shaped to convex, it flattens during maturity, developing visible surface grooves corresponding to the gills underneath the cap. The margin of the cap has minute but distinct scallops.
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The small, diaphanous shell has an elongate-conic shape. Its length measures 3.2 mm. The 2½ whorls of the protoconch are small and helicoid. They form a moderately elevated spire, with their axis at right angles to that of the succeeding turns, in the first of which they are about one-fifth immersed.
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The shell is very large, solid, rimate, ovate-conic. The spire is subregularly tapering and the penultimate whorl is somewhat bulging. The last whorl is depressed on the back. The color of the shell is dark reddish-brown or rich chestnut with narrow darker streaks and a lighter margin below the suture.
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The height of the shell attains 1 mm, its diameter 0.9 mm. The very small, white shell is umbilicate, turbinate, not nacreous, with a conic brownish spire. The first whorl appears to be smooth. On the second whorl fine radial folds or puckering appears below the suture, becoming coarser on the following whorl.
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The shell in this genus is small, ovate-conic, thin and translucent. The protoconch is heterostrophic and smooth, and it is obliquely immersed in the first adult whorl. The adult shell has a sculpture of spiral cords which are separated by deep grooves. The spiral cords have numerous transverse threads in their intervals.
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The spire is conic. The apex is acute. The 10 whorls are spirally encircled by numerous (about 10 on upper surface) beaded lirae, which are separated by superficial interstices. Above the sutures there is a series of short folds or knobs which usually become obsolescent upon the periphery of the body whorl.
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The base of the shell is similarly variegated, but the dots are sometimes brown. Furrows between the bead-rows are finely and densely decussate by spiral and oblique raised striae or threads. The spire is straightly conic with an acute, roseate apex and about six whorls. The body whorl is deflexed in front.
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The milk-white shell has a conic shape. Its length measures 3 mm. The 2½ whorls of the protoconch are well rounded. They form a depressed helicoid spire, the axis of which is at right angles to that of the succeeding turns, in the first of which it is about one-third immersed.
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The Pileus is 1.4–3.5 cm in diameter and conic to convex to broadly convex then becoming flat in age. It is not usually umbonate. The pileus is deep chestnut brown and hygrophanous, fading to yellowish brown or grayish white when dry. The surface is viscid when moist from the separable gelatinous pellicle.
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The small, white shell grows to a length of 3 mm. It is elongate-conic, slender, slightly umbilicated. The at least two whorls of the protoconch are obliquely about half immersed in the first of the later whorls. The six whorls of the teleoconch are flattened, with strong tabulated and crenulated summits.
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V. Protasov, R. M. Jungers, and V. D. Blondel. "Joint spectral characteristics of matrices: a conic programming approach." SIAM Journal on Matrix Analysis and Applications, 2008. The advantage of these methods is that they are easy to implement, and in practice, they provide in general the best bounds on the joint spectral radius.
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The word "hyperbola" derives from the Greek , meaning "over-thrown" or "excessive", from which the English term hyperbole also derives. Hyperbolae were discovered by Menaechmus in his investigations of the problem of doubling the cube, but were then called sections of obtuse cones.. The term hyperbola is believed to have been coined by Apollonius of Perga (c. 262–c. 190 BC) in his definitive work on the conic sections, the Conics. The names of the other two general conic sections, the ellipse and the parabola, derive from the corresponding Greek words for "deficient" and "applied"; all three names are borrowed from earlier Pythagorean terminology which referred to a comparison of the side of rectangles of fixed area with a given line segment.
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The shell has an elongate-conic shape. it is creamy yellow, with a narrow, golden brown band situated about one-fourth of the distance between the apex and suture posterior to the suture. (The whorls of the protoconch are decollated). The whorls of the teleoconch are slightly rounded, and feebly shouldered at the summit.
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It is not reasonable to formally extend the definition of quadrics to spaces over genuine skew fields (division rings). Because one would get secants bearing more than 2 points of the quadric which is totally different from usual quadrics. R. Artzy: The Conic y=x^2 in Moufang Planes, Aequat.Mathem. 6 (1971), p. 31-35E.
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The cap is up to 5 cm across, grayish brown, not hygrophanous, conic to campanulate in age. The cap margin is not adorned with remnants of the partial veil. The stem is 10 cm by 2.5 mm, fibrous and pruinose. The gills are adnexed and close, with one or two tiers of intermediate gills.
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The size of the shell attains 15 mm. The rather thick, imperforate shell has a conic-elongate shape. The 6 to 7 whorls are planulate, the first buff, eroded, the following whitish, ornamented with sparse rosy points and angular chestnut streaks . The shell is spirally lirate, with about 8 lirae on the penultimate whorl.
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P. arizonae is a small snail that has a height of and a globose to elongate conic shell. Its differentiated from other Pyrgulopsis in that its penial filament has an elongate lobe and medium length, broad filament with the penial ornament consisting of a large, superficial ventral gland often with a similar dorsal gland.
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Ghetaldi was the constructor of the parabolic mirror (66 cm in diameter), kept today at the National Maritime Museum in London. He was also a pioneer in making conic lenses. During his sojourn in Padua he met Galileo Galilei, with whom he corresponded regularly. He was a good friend to the French mathematician François Viète.
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The size of the shell varies between 6 mm and 10 mm. The umbilicate shell has a globose-conic shape. It is coral-red or brown, marked beneath the sutures with narrow flames of white and maculations of brown, and on the base dotted with white. But the species exhibits a considerable variation in color.
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The height of the shell varies between 25 mm and 30 mm. The thick, imperforate or very narrowly perforate shell has a conic-elongated shape. It is whitish, ornamented with radiating livid-brown flammules, brown punctulate. The 9 whorls are convex, spirally lirate (the lirae unequal) and longitudinally nodose-costate, the nodules more prominent below.
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The size of the shell varies between 25 mm and 65 mm. This is an excessively variable form. The solid, heavy shell has a conical shape and is falsely umbilicate. The spire is strictly conic, or swollen and somewhat convex below, acuminate above, or sometimes constricted around the upper part of the body whorl.
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The milk-white shell has an elongate-conic, turreted shape. Its length measures 4.4 mm. The three whorls of the protoconch are small, helicoid, rather loosely coiled and elevated. They have their axis at a right angle to the axis of the later whorls and about one-third immersed in the first of them.
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The broadly elongate- conic shell is turreted and subdiaphanous. It measures 2.6 mm. The whorls of the protoconch are small, almost completely obliquely immersed, only part of the last rounded volution is visible above the first of the later whorls. The 5½ whorls of the teleoconch are somewhat inflated, well rounded and moderately shouldered.
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Theorem 1.1.) It is not known whether varieties with these properties exist over the algebraic closure of the rational numbers. Uniruledness is a geometric property (it is unchanged under field extensions), whereas ruledness is not. For example, the conic x2 \+ y2 \+ z2 = 0 in P2 over the real numbers R is uniruled but not ruled.
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The size of the shell varies between 6 mm and 11 mm. The small shell is depressed and umbilicate. It is pinkish brown, gray or yellow, the ribs articulated with dots of black and white, often forming radiating lines above, zigzag beneath, where yellow replaces pink in the ground-color. The spire is low-conic.
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The height of the shell attains 6 mm, its major diameter also 6 mm. The small, solid shell has a globose-conic shape. It has a carmine colour with radial buff dashes, about eight to a whorl, reaching from the suture half-way to the periphery. The umbilicus and the bordering funicle is white.
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The length of the shell varies between 20 mm and 25 mm. The thick, imperforate or very narrowly perforate shell has a conic-elongated shape. It is whitish, ornamented with radiating livid-brown flammules, brown punctulate. The 9 whorls are convex, spirally lirate (the lirae unequal) and longitudinally nodose-costate, the nodules more prominent below.
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A tri-axial equivalent of the Mercator projection was developed by John P. Snyder. Equidistant map projections of a tri-axial ellipsoid were developed by Paweł Pędzich. Conic Projections of a tri-axial ellipsoid were developed by Maxim Nyrtsov. Equal- area cylindrical and azimuthal projections of the tri-axial ellipsoid were developed by Maxim Nyrtsov.
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The white shell has a broadly conic shape. Its length measures 3.1 mm. The whorls of the protoconch are smooth, largely obliquely immersed in the first of the succeeding turns above, which only about half of the last turn projects. The five whorls of the teleoconch are moderately rounded, slopingly shouldered at the summit.
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The base of the shell scores by 5 or 6 narrow, spaced, concentric grooves that become stronger near the axis. The conic spire contains 6½ convex whorls. The body whorl is subangular at the periphery and convex beneath. The oblique aperture is brilliantly green inside, with a dusky submarginal band and a pale edge.
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Two or three of these spiral lines ascend the spire. Its sculpture consists of slight growth lines and fainter or wholly obsolete fine spiral striae above, and about 6 fine-spaced grooves around the umbilical region, stronger toward the middle. The conic spire has an acute apex. The about 6½ whorls are quite convex.
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Smith, Sakabe was a student of Ajima Naonobu.Hatashi, T. [Hayashi Tsuruichi?] "The Conic Sections in the Old Japanese Mathematics," Hayashi, Tsuruichi. (1907). "A Brief history of the Japanese Mathematics," Sakabe investigated some European and Chinese works which had appeared in Japan, but his general method was later construed to be innovative, clarified and thus improved.
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The size of the shell varies between 50 mm and 80 mm. The large, heavy, solid, imperforate shell has an ovate-conic shape. Its color pattern is dirty white, or greenish, maculated with angular, alternating blackish or brown and light patches on the broad flat spiral ribs. The interstices are narrow, superficial, and whitish.
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The light-yellow shell has an elongate-conic shape. lts length measures 3.8 mm. The whorls of the protoconch are deeply obliquely immersed in the first of the succeeding turns. The six whorls of the teleoconch are cylindric in outline, moderately rounded in the middle and very much so at the very strongly shouldered summit.
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The conic shell is, milk-white. It measures 2.0 mm. The whorls of the protoconch number at least two, forming a depressed helicoid spire, which is slightly tilted to one side and for the greater part immersed in the first of the succeeding turns. The tilted edge of the nucleus shows traces of spiral lirations.
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The bluish-white shell is moderately large, measuring 3.1 mm. Its shape is very elongate-ovate, with a very regular, conic spire. The nuclear whorls are small, obliquely immersed in the first of the succeeding turns, above which a portion of the last two volutions only project. The six post-nuclear whorls are flattened.
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The large, broadly conic shell measures 6.6 mm. It is milk- white and shining. The whorls of the protoconch are deeply obliquely immersed in the first of the succeeding turns, above which only the tilted edge of the last volution projects. The seven whorls of the teleoconch are moderately rounded, somewhat shouldered at the summit.
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The technology is characterized by stable states i.e. focal conic state (dark state) and planar state (bright state). Displays based on this technology are called “bistable” and don’t need any power to maintain the information (zero power). Because of the reflective nature of the ChLCD, these displays can be perfectly read under sunlight conditions.
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The broadly conic shell is bluish-white. It measures 4.5 mm. The nuclear whorls are deeply obliquely immersed in the first of the succeeding turns, above which only the tilted edge of the last volution projects. The six post-nuclear whorls are well rounded, slightly contracted at the suture and appressed at the summit.
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The milk-white shell is very slender and has an elongate- conic shape. The shell grows to a length of 2.7 mm. The 1¾ whorls of the protoconch are depressed, and helicoid. Their axis is at right angles to that of the succeeding turns, in the first of which they are very slightly immersed.
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Gustav Conrad Bauer (18 November 1820, Augsburg – 3 April 1906, Munich) was a German mathematician, known for the Bauer-Muir transformation and Bauer's conic sections. He earned a footnote in the history of science as the doctoral advisor (Doktorvater) of Heinrich Burkhardt, who became one of the two referees of Albert Einstein's doctoral dissertation.
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Considering the evidence of Orkhon inscriptions that every balbal represented a certain person, such distinction cannot be by chance. Likely here is marked an important ethnographic attribute, a headdress. The steppe-dwellers up until present wear a conic 'malahai', and the Altaians wear flat round hats. The same forms of headdresses are recorded for the 8th century.
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Bang Your Head: The Rise and Fall of Heavy Metal. Three Rivers Press, 2002. p. 239 The album reached number two on the indie album chart and number 40 in the UK Album Chart. In the early 1980s, "[i]conic punk fanzines like Flipside, which could make or break [band] reputations, pronounced them [Discharge] "fucking great.
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They contain powers of 1 or 2 respectively. Apollonius had not much use for cubes (featured in solid geometry), even though a cone is a solid. His interest was in conic sections, which are plane figures. Powers of 4 and up were beyond visualization, requiring a degree of abstraction not available in geometry, but ready at hand in algebra.
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The light brown, shining shell has an elongate-conic shape. The length of the shell measures 17.6 mm. The 2½ whorls of the protoconch are small and polished, and have a depressed helicoid shape. Their axis is at a right angle to the axis of the later whorls and about one-sixth immersed in the first of them.
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The base of the body whorl is adorned with fine spiral threads, close together upon the beak. The whole sculpture is crossed by very fine, strongly flexuous, and oblique growth lines. The spire is high, conic, somewhat less than twice the height of the aperture. The protoconch consists of 2 whorls, which are microscopically spirally striate.
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Because of the essential role of the circle (considered as the non-degenerate conic in a projective plane) and the plane description of the original models the three types of geometries are subsumed to planar circle geometries or in honor of Walter Benz, who considered these geometric structures from a common point of view, Benz planes.
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Turner 1997, pp.43–61 Omar Khayyam's "Cubic equation and intersection of conic sections" Al-Khwarizmi (8th–9th centuries) was instrumental in the adoption of the Hindu-Arabic numeral system and the development of algebra, introduced methods of simplifying equations, and used Euclidean geometry in his proofs. Toomer, Gerald (1990). "Al-Khwārizmī, Abu Jaʿfar Muḥammad ibn Mūsā".
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These all have positive Gaussian curvature. The third case generates the hyperbolic paraboloid or the hyperboloid of one sheet, depending on whether the plane at infinity cuts it in two lines, or in a nondegenerate conic respectively. These are doubly ruled surfaces of negative Gaussian curvature. The degenerate form :X_0^2-X_1^2-X_2^2=0.
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There are 2–3 tiers of lamellulae interspersed between the gills. The cap of M. cinerella is white and small, with a diameter typically ranging from . Initially hemispherical, obtusely conic, and then convex, it expands during maturity, developing visible grooves on the surface that correspond to the gills underneath the cap. The cap has a broad, flattened umbo.
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A number of color models exist in which colors are fit into conic, cylindrical or spherical shapes, with neutrals running from black to white along a central axis, and hues corresponding to angles around the perimeter. Arrangements of this type date back to the 18th century, and continue to be developed in the most modern and scientific models.
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Geometry has many applications in architecture. In fact, it has been said that geometry lies at the core of architectural design. Applications of geometry to architecture include the use of projective geometry to create forced perspective, the use of conic sections in constructing domes and similar objects, the use of tessellations, and the use of symmetry.
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The milk-white shell has a conic shape. (The whorls of the protoconch are decollated.) The length of the shell measures just over 5 mm. The ten whorls of the teleoconch are moderately well rounded, and very slightly shouldered at the summit. They are marked by mere indications of obsolete ribs near the summit of the early whorls, only.
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The very slender, diaphanous to milk-white shell has an elongate-conic shape. Its length measures 4.4 mm. The 2½ whorls of the protoconch are small. They form a small elevated helicoid spire, the axis of which is at right angles to that of the succeeding turns, in the first of which it is about one-third immersed.
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The small shell has a conic shape. Its color is light chestnut, with the umbilical area white. Its length is 2.9 mm. The 2½ whorls of the protoconch form a depressed helicoid spire, whose axis is at right angles to that of the succeeding turns, in the first of which it is about one- third immersed.
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The shell has an elongate-conic shape. The anterior half of whorls is chestnut brown, the rest flesh colored. The length of the shell measures 7.2 mm. The two whorlsof the protoconch form a depressed helicoid spire, whose axis is at right angles to that of the succeeding turns, in the first of which it is one-fifth immersed.
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The pale yellowish brown shell has an elongate conic shape . Its length measures 6.1 mm. The 2½ whorls of the protoconch are well rounded. They form a very depressed helicoid spire, the axis of which is at right angles to that of the succeeding turns in the first of which it is about one- fourth immersed.
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The pale yellow horn-colored shell has a broadly elongate conic shape. Its length measures 5.5 mm. The 2½ whorls of the protoconch are well rounded. They form a decidedly depressed helicoid spire having its axis at right angles to that of the succeeding whorls, in the first of which, the tilted edge is about one-fourth immersed.
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The milk-white shell has a very broadly conic shape. The length of the shell is 2.8 mm. It is tabulatedly shouldered. The 2½ whorls of the protoconch form a decidedly elevated spire, the axis of which is at right angles to that of the succeeding turns, in the first of which it is slightly immersed.
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The fasciole on the beak is finely striated. Sometimes the spiral sculpture is predominant, the spirals becoming much stronger, crossed only by flexuous axial strife. The colour of the shell is light flavescent with a white band encircling the whorls, but mostly inconspicuous. The spire is high, conic, turreted, about 1½ times the height of the aperture.
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The creators of HSL and HSV were far from the first to imagine colors fitting into conic or spherical shapes, with neutrals running from black to white in a central axis, and hues corresponding to angles around that axis. Similar arrangements date back to the 18th century, and continue to be developed in the most modern and scientific models.
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Conics may be defined over other fields (that is, in other pappian geometries). However, some care must be used when the field has characteristic 2, as some formulas can not be used. For example, the matrix representations used above require division by 2. A generalization of a non- degenerate conic in a projective plane is an oval.
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Left – Lead reactor core with conic void. Right – Observed core where average scattering angles of muons are plotted. The void in the core is clearly imaged through two 2.74 m concrete walls. The lead core of 0.7 m thickness gives an equivalent radiation length to the uranium fuel in Unit 1, and gives a similar scattering angle.
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The bluish white shell is rather large, its length measuring 5.8 mm. It has an elongate conic shape. The whorls of the protoconch are obliquely immersed in the first of the succeeding turns, above which the tilted edge of the last volution only projects. The almost seven whorls of the teleoconch are moderately rounded, and appressed at the summit.
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Relativity: An Introduction to the Special Theory, pp. 5–10. World Scientific. . Although this may be the first suggestion that a conic section could play a role in astronomy, al-Zarqālī did not apply the ellipse to astronomical theory and neither he nor his Iberian or Maghrebi contemporaries used an elliptical deferent in their astronomical calculations.
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Large inns, made of stone or bricks, were built. Those caravan stations had vast inner yards with horse stables and storages for the transported goods. They had upper floors, roofed with lead or conic tiles (ćeramida), where sleeping chambers with fireplaces were located. Rooms were vaulted, and sometimes both beds and fireplaces were built from bricks.
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The crown is broadly conic, while the brownish bark is scaly and deeply fissured, especially with age. The twigs are a yellow-brown in color with darker red- brown pulvini, and are densely pubescent. The buds are ovoid in shape and are very small, measuring only in length. These are usually not resinous, but may be slightly so.
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More generally, there are infinitely many cubics that pass through the nine intersection points of two cubics (Bézout's theorem implies that two cubics have, in general, nine intersection points) Likewise, for the conic case of n = 2, if three of five given points all fall on the same straight line, they may not uniquely determine the curve.
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The bluish-white shell has an elongate-conic shape. Its length measures 5.3 mm. The whorls of the protoconch are almost completely obliquely immersed in the first of the succeeding turns, above which only the outer edge of the last volution projects. The six whorls of the teleoconch are rather high between the sutures, moderately rounded.
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Lam Chun Kiu later also founded his own electronics company, including a joint venture that now known as Konka Group (). Since then, Conic Investmnent was shifted its focus to the mainland China under the new owner. Sin King also attempted to privatise and delist the company in 1987. However, the plan was abandoned in the same year.
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The focus–directrix property of the parabola and other conic sections is due to Pappus. Galileo showed that the path of a projectile follows a parabola, a consequence of uniform acceleration due to gravity. The idea that a parabolic reflector could produce an image was already well known before the invention of the reflecting telescope. Extract of page 3.
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The milk-white, shining shell has an elongate-conic shape. Its length measures a little more than 6 mm. The 2½ whorls of the protoconch are very small. They form a rather elevated spire, having their axis at right angles to that of the succeeding turns, in the first of which they are about one-fourth immersed.
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The height of the shell attains 9 mm, its diameter 10 mm. The oblique, imperforate shell has an orbiculate-conic shape and is slightly elevated. The base of the shell is very wide. The shell is longitudinally very obliquely subtly striate, and marked with a few spiral subimpressed lines which are sometimes obsolete, leaving the surface smooth.
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The height of the shell varies between 12 mm and 18 mm. The solid, imperforate, acute shell has an elongate-conic shape. It is polished, grayish or pinkish, with a few spiral orange lines, two on the penultimate whorl. The spaces between these lines marked with short white curved lines in pairs, often forming a figure 8 shaped pattern.
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21 (1962), pp. 37–59. # An oval in a pappian projective plane of characteristic is a conic if and only if for any point of a tangent there is an involutory perspectivity (symmetry) with center which leaves invariant.H. Mäurer: Ovoide mit Symmetrien an den Punkten einer Hyperebene, Abh. Math. Sem. Hamburg 45 (1976), pp. 237–244.
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The white shell has an elongate-conic shape. Its length measures 4.8 mm. The whorls of the protoconch are deeply obliquely immersed in the first of the succeeding turns, above which only the titled edge of the last volution projects. The six whorls of the teleoconch are well rounded, rather high between the sutures, contracted at the periphery.
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The lacy elimia is a small species in the family Pleuroceridae. Growing to about 1.1 centimeters (cm) (0.4 in) in length, the shell is conic in shape, strongly striate, and often folded in the upper whorls. The shell color is dark brown to black, often purple in the aperture, and without banding. The aperture is small and ovate.
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Stimpson (1865) described the genus as follows: “Shell ovate- conic, imperforate; apex acute; whorls coronated with spines; outer whorl nearly two-thirds the length of the shell; aperture ovate, outer lip acute. Operculum corneous, subspiral. Foot rather short for the length of the shell, broadest in front and strongly auriculated. Tentacles very long, slender, and tapering.
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P. davisi is a small snail that has a height of and an ovate to narrowly conic, medium-sized shell. Its differentiated from other Pyrgulopsis in that its penial filament has a medium length lobe and medium length filament with the penial ornament consisting of an elongate, proximally bifurcate, penial gland; curved, transverse terminal and ventral glands.
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The cap is typically 7-15 mm in diameter, almost convex to conic in shape, umbonate with a small papilla. The cap is viscid and has a separable pellicle. It is a reddish-brown color when moist, but becomes lighter brown when dry. The stipe is 4.0-6.5 cm high × 1.5 cm thick, equal or slightly bulbous.
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The cones grow on bare peduncles 7–15 mm in length and produce two smooth brown oval-shaped seeds. Cone maturation occurs from March to April. The plant forms conic terminal buds 1–3 mm in length. Mature female cones are sometimes mistaken for flowers at a distance, as they appear in groups of several cones at stem joints.
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A large portion of the math section is problem-solving, in which students are required to both analyze and draw conclusions from numerical data (like graphs and charts) or compute answers to a problem using previous mathematical knowledge. The other portion of the exam requires knowledge in advanced topics like calculus, algebra, trigonometry, probability, and conic sections.
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The pores are large, angular, and arranged radially. The cap of the fruit body is in diameter, and depending on its age, is either conic to convex, to somewhat flattened at maturity. The cap margin is initially rolled downward before straightening out, often with hanging remnants of partial veil (appendiculate).Bessette et al. (2001), pp. 246–47.
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The palatine uvula, usually referred to as simply the uvula, is a conic projection from the back edge of the middle of the soft palate, composed of connective tissue containing a number of racemose glands, and some muscular fibers.Ten Cate's Oral Histology, Nanci, Elsevier, 2007, page 321 It also contains many serous glands, which produce thin saliva.
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The very regularly elongate-conic shell is subdiaphanous to milk-white. Its length measures 5.6 mm. The whorls of the protoconch are small, deeply obliquely immersed in the first of the succeeding turns, above which the tilted edge of the last turn only is visible. The seven whorls of the teleoconch are slightly rounded, and separated by constricted sutures.
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The elongate-conic shell is white. Its length measures 2.5 mm. The two whorls of the protoconch are deeply, obliquely immersed in the first of the succeeding turns. The six whorls of the teleoconch are marked by two strongly elevated tuberculate keels between the sutures, the posterior one of which is about twice as wide as its neighbor.
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The soiled white shell is elongate-conic. It measures 4.8 mm. The at least two whorls of the protoconch are moderately large, helicoid, one-half obliquely immersed in the first volution of the teleoconch, the periphery projecting slightly beyond the left outline of the spire. The six whorls of teleoconch are well rounded, very slightly shouldered.
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The white, ovate-conic shell measures 1.8 mm. The nuclear whorls are moderately large, obliquely deeply immersed in the first post- nuclear whorl, the peripheral portion only of the last volution projects above the edge. The four post-nuclear whorls are moderately rounded, and the shoulders are strongly crenelated. They are marked between the sutures by four spiral keels.
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The elongate-conic shell is milk-white. It measures 4.3 mm. The whorls of the protoconch number at least two, and are small, smooth, and obliquely half immersed in the first of the succeeding turns. The seven and one-half whorls of the teleoconch are well rounded, moderately contracted at the suture, and well shouldered at the summit.
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The conic shell is milk-white. Its length measures 4.2 mm. The whorls of the protoconch are smooth, deeply obliquely immersed in the first of the succeeding whorls, above which only a portion of the last two volutions project. The six whorls of the teleoconch are moderately rounded, slightly contracted at the sutures, feebly shouldered at the summits.
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The elongate-conic shell is thick and heavy, rough through erosion, yellowish white. Its length measures 9.9 mm. The whorls of the protoconch are decollated in the type, judging from the pit in the apex they are probably deeply, obliquely immersed. The six whorls of the teleoconch are only moderately rounded, somewhat shouldered at the summit (surface decidedly eroded).
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The generally slender, bluish-white to milk-white, semitranslucent shell is more or less elongated and has a cylindro-conic shape. The apex is sinistral. The reversed, flattened or projecting protoconch consists of 1½ to 3 whorls that are oblique or tilted from transverse to the axis. The teleoconch contains many planulate or more or less convex whorls.
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If six unordered points are given on a conic section, they can be connected into a hexagon in 60 different ways, resulting in 60 different instances of Pascal's theorem and 60 different Pascal lines. This configuration of 60 lines is called the Hexagrammum Mysticum. with a reference to Veblen and Young, Projective Geometry, vol. I, p.
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The affine part of the generated curve appears to be the hyperbola y=1/x. Remark: #The Steiner generation of a conic section provides simple methods for the construction of ellipses, parabolas and hyperbolas which are commonly called the parallelogram methods. #The figure that appears while constructing a point (figure 3) is the 4-point-degeneration of Pascal's theorem.
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The height of the shell varies between 8.9 mm, its diameter 10.5 mm. The shell has a shiny surface. Its color is dingy white, with broad radiating flames of brown or red above irregularly maculated below, sometimes nearly unicolored, pinkish, with the lirae of the base articulated with red and white dots. The spire is either conic or depressed.
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The size of the shell varies between 15 mm and 36 mm. Rather low-conic shell is conspicuously radiately plicate above. The folds are somewhat sigmoid and oblique, bearing a series of short rounded knobs above, and terminating in short spines, eighteen to twenty in number, at the carinated periphery. The base of the shell is flat, squamosely lirate.
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The subdiaphanous to milk-white shell is slender and has an elongate-conic shape. Its length measures 3.3 mm. The whorls of the protoconch are immersed, the last one only being visible. This is somewhat tilted and marked by three strong narrow spiral keels and many slender raised axial threads which cross the grooves between the keels.
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The yellowish white shell has a regularly, broadly elongate conic shape. Its length measures 5.2 mm. The 2½ smooth whorls of the protoconch form a decidedly depressed helicoid spire. Its axis is at right angles to that of the succeeding turns in the first of which about one-fourth of the side of the spire is immersed.
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The bluish white shell has an elongate conic shape. The length of the shell measures 7.4 mm. The teleoconch of the type specimen contains 11½ whorls, marked by very fine, closely spaced, incised spiral lines. The short, rounded base of the shell shows rather strong incremental lines and the same spiral sculpture as seen on the spire.
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Eccentricity, which is a mathematical constant conveyed in the form of a ratio and essentially describes to what degree a conic section deviates from being circular. Another variable that impacts motion silencing, eccentricity determines to what extent motion causes silencing. Choi, Bovik, and Cormack (2016) observed that when eccentricity in peripheral vision increases, motion silencing decreases.
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Then no five points of and no three points of are collinear. Since will always contain the whole line through on account of Bézout's theorem, the vector space of cubic homogeneous polynomials that vanish on (the affine cones of) is isomorphic to the vector space of quadratic homogeneous polynomials that vanish (the affine cones of) , which has dimension two. Although the sets of conditions for both dimension two results are different, they are both strictly weaker than full general positions: three points are allowed to be collinear, and six points are allowed to lie on a conic (in general two points determine a line and five points determine a conic). For the Cayley-Bacharach theorem, it is necessary to have a family of cubics passing through the nine points, rather than a single one.
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The conic sections have some very similar properties in the Euclidean plane and the reasons for this become clearer when the conics are viewed from the perspective of a larger geometry. The Euclidean plane may be embedded in the real projective plane and the conics may be considered as objects in this projective geometry. One way to do this is to introduce homogeneous coordinates and define a conic to be the set of points whose coordinates satisfy an irreducible quadratic equation in three variables (or equivalently, the zeros of an irreducible quadratic form). More technically, the set of points that are zeros of a quadratic form (in any number of variables) is called a quadric, and the irreducible quadrics in a two dimensional projective space (that is, having three variables) are traditionally called conics.
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In 1993 Conic Investment was acquired by fellow SOE China Aerospace Science and Technology Corporation (CASC) as a backdoor listing, renaming to China Aerospace International Holdings Limited (). The English name of the company was remained unchanged since 1993, but the Chinese name had changed to the current one in 2008. Some of the subsidiaries of former Conic Investment remained intact as live subsidiaries, although the economic transformation of Hong Kong had made most of the factories of the group were shifted to mainland China. In 2000, the Stock Exchange of Hong Kong publicly criticised four (former) directors of CASIL for not disclosing related-parties deals of CASIL and CASC properly, as well as disclosing the deals with XCOM Multimedia Communications, a company that owned a stake in CASIL's joint venture CXSAT.
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Furthermore, the four base points determine three line pairs (degenerate conics through the base points, each line of the pair containing exactly two base points) and so each pencil of conics will contain at most three degenerate conics.. A pencil of conics can be represented algebraically in the following way. Let and be two distinct conics in a projective plane defined over an algebraically closed field . For every pair of elements of , not both zero, the expression: ::\lambda C_1 + \mu C_2 represents a conic in the pencil determined by and . This symbolic representation can be made concrete with a slight abuse of notation (using the same notation to denote the object as well as the equation defining the object.) Thinking of , say, as a ternary quadratic form, then is the equation of the "conic ".
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In mathematics, a projective range is a set of points in projective geometry considered in a unified fashion. A projective range may be a projective line or a conic. A projective range is the dual of a pencil of lines on a given point. For instance, a correlation interchanges the points of a projective range with the lines of a pencil.
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The spiral below the suture is a little stronger than the others; frequent inequidistant faint growth periods form the only axial sculpture. The colour of the shell is whitish, the protoconch light violet. The spire is elevated, conic, about 1½ times the height of the aperture. The protoconch consists of 1¾ whorls, smooth, globose, the nucleus flatly convex, slightly lateral.
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Osborn Maitland Miller (1897–1979) was a Scottish-American cartographer, surveyor and aerial photographer. A member of several expeditions himself, he also acted as adviser to other explorers. He developed several map projections, including the Bipolar Oblique Conic Conformal, the Miller Oblated Stereographic, and most notably the Miller Cylindrical in 1942. The Maitland Glacier in Antarctica was named after Miller in 1952.
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The summit of Conic Hill with; in the background its sub-summit at It is on the east bank of Loch Lomond, beside the village of Balmaha. It is a sharp little summit which is on the Highland Boundary Fault. There was a tiny cairn at the top (); there is only a scattering of stones to mark the "true" summit.Conic Hill at www.
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In general the determination of an intersection leads to non-linear equations, which can be solved numerically, for example using Newton iteration. Intersection problems between a line and a conic section (circle, ellipse, parabola, etc.) or a quadric (sphere, cylinder, hyperboloid, etc.) lead to quadratic equations that can be easily solved. Intersections between quadrics lead to quartic equations that can be solved algebraically.
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The small, almost translucent shell has an elongate-conic shape. Its length measures 3.7 mm. The whorls of the protoconch are small, very obliquely immersed in the first of the succeeding turns, above which the rounded, tilted edge of the last volution only projects. The six whorls of the teleoconch are high between the sutures, slightly rounded, and feebly shouldered at the summit.
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In astrodynamics, the patched conic approximation or patched two-body approximationBate, R. R., D. D. Mueller, and J. E. White [1971], Fundamentals of Astrodynamics. Dover, New York.Lagerstrom, P. A. and Kevorkian, J. [1963], Earth-to-moon trajectories in the restricted three-body problem, Journal de mecanique, p. 189-218. is a method to simplify trajectory calculations for spacecraft in a multiple-body environment.
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The light yellow horn-colored shell has an elongate conic shape. Its length measures 4.8 mm. The 2½ whorls of the protoconch are well rounded. They form a decidedly depressed helicoid spire, the axis of which is at right angles to that of the succeeding whorls, in the first of which the tilted edge of the nucleus is about one-fifth immersed.
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Conocybe tenera is a small saprotrophic mushroom with a conic to convex cap and is smooth and colored cinnamon brown. It is usually less than 2 cm across and is striate almost to the center. The gills are adnate and colored pale brown, darkening in age. The spores are yellowish brown, smooth and ellipsoid with a germ pore, measuring 12 x 6 micrometres.
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The mathematical theory of origami is more powerful than straightedge and compass construction. Folds satisfying the Huzita–Hatori axioms can construct exactly the same set of points as the extended constructions using a compass and conic drawing tool. Therefore, origami can also be used to solve cubic equations (and hence quartic equations), and thus solve two of the classical problems.
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The front sensors are bipolar and the second conic feature, the rear sensor, has eight sensilla. The cephalopharyngeal skeleton has very short dorsal and ventral apodemes, the hypostomal scleritis is triangular. It lacks a subhypostomal and the jaws are hooked. The oral lobes have 10–12 indents, preceded on each side by a sensory plate similar to the larva of the Ceratitis capitata.
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The elongate-conic shell has a light yellowish-brown color, excepting the umbilical area, the extreme basal portion and the tip, which are white. The shell measures 3 mm. The whorls of the protoconch are very small. Their sculpture is decorated with spiral ribs in contrast to almost all species in Pyramidellidae where the sculpture of the protoconch is smooth.
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According to Bézout's theorem, two different cubic curves over an algebraically closed field which have no common irreducible component meet in exactly nine points (counted with multiplicity). The Cayley-Bacharach theorem thus asserts that the last point of intersection of any two members in the family of curves does not move if eight intersection points (without seven co-conic ones) are already prescribed.
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Apollonius's work was translated into Arabic, and much of his work only survives through the Arabic version. Persians found applications of the theory, most notably the Persian mathematician and poet Omar Khayyám, who found a geometrical method of solving cubic equations using conic sections.Boyer, C. B., & Merzbach, U. C., A History of Mathematics (Hoboken: John Wiley & Sons, Inc., 1968), p. 219.
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Table tennis rubber has four common types: inverted and short pips rubber are primarily offensive, while long pips and antispin are primarily defensive. The word "pip" refers to the usually conic- shaped raised bumps on top of the rubber in short and long pips rubber or the bumps on the inside attached to the foam on inverted or antispin rubber.
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Built in the 11th century AD, Imamzadeh Jafar is one of the few examples of the architecture of the Seljuq and Ilkhanid eras in Iran. A very similar mausoleum is the Tomb of Daniel in Susa, south western Iran. The building is octagonal with a high dome in the center. The height of the conic-shaped dome is 25 meters from the base.
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The small shell has an elongate-conic shape. Its length measures 2.5 mm. The whorls of the protoconch are small, smooth, and strongly obliquely immersed in the first of the succeeding turns, above which only the tilted edge of the last volution projects. The five whorls of the teleoconch are moderately rounded, strongly contracted at the sutures, and slopingly shouldered at the summit.
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The cap is in diameter, conic when young, bell-shaped to convex or plano-convex when mature, and umbonate. The cap margin is curved downward, even or slightly eroded. The red-orange cap surface is dry to moist, and wrinkled towards the margin but smooths out as it approaches the center. Sometimes there is white-yellowish flesh underneath the cap cuticle.
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Tsuga mertensiana is a large evergreen coniferous tree growing to tall, with exceptional specimens as tall as tall. They have a trunk diameter of up to . The bark is thin and square-cracked or furrowed, and gray in color. The crown is a neat, slender, conic shape in young trees with a tilted or drooping lead shoot, becoming cylindric in older trees.
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In enumerative geometry, Steiner's conic problem is the problem of finding the number of smooth conics tangent to five given conics in the plane in general position. If the problem is considered in the complex projective plane CP2, the correct solution is 3264 (). The problem is named after Jakob Steiner who first posed it and who gave an incorrect solution in 1848.
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The Fermat curve is non-singular and has genus :(n - 1)(n - 2)/2.\ This means genus 0 for the case n = 2 (a conic) and genus 1 only for n = 3 (an elliptic curve). The Jacobian variety of the Fermat curve has been studied in depth. It is isogenous to a product of simple abelian varieties with complex multiplication.
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The height of the shell attains 11 mm, its diameter 14 mm. The umbilicate shell has a depressed-globose conic shape. It is, polished, shining, blackish, olive or purplish brown, unicolored, dotted or tessellated with white, often with short flames of white beneath the sutures and always more or less marked with white around the umbilicus . The spire is conical.
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However, in a pappian projective plane a conic is a circle only if it passes through two specific points on the line at infinity, so a circle is determined by five non-collinear points, three in the affine plane and these two special points. Similar considerations explain the smaller than expected number of points needed to define pencils of circles.
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The height of the shell varies between 8 mm and 13 mm. The conic shell is well elevated. Its color is pale yellowish or reddish-brown, with broad dark brown oblique flammules. It is anteriorly somewhat articu-ated with red and yellowish-white in fine concentric lines with many elevated granulous spiral lines, of which three larger are next above the suture.
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He left Durham at the beginning of 1762 to become minister at Filby, Norfolk, and assistant to John Whiteside (died 1784) at Great Yarmouth. Here he resumed his intimacy with Manning, now practising as a physician at Norwich. He began his treatise on conic sections, suggested to him by Isaac Newton's Arithmetica Universalis, 1707. He took pupils in mathematics and navigation.
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There is evidence they also traded wild animal skins with Black Sea towns. Some sites were defended by ditches and banks, structures thought to have been built to defend against nomadic tribes from the steppe.Mallory. EIEC. Page 657 Dwellings were either of surface or semi-subterranean types, with posts supporting the walls, a hearth in the middle, and large conic pits located nearby.
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The vitreous shell has a conic shape. Its length measures 3.4 mm. The whorls of the protoconch are small, smooth, obliquely deeply immersed in the first of the succeeding turns, above which only the tilted edge of the last volution projects. The six whorls of the teleoconch are flattened, strongly contracted at the periphery and moderately shouldered at the summit.
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The white shell has a very elongate-conic shape. Its length measures 3.1 mm. The two whorls of the protoconch form a moderately elevated helicoid spire which is about one-half obliquely immersed in the first of the succeeding turns. The six whorls of the teleoconch are almost flattened, strongly contracted at the suture and strongly shouldered at the summit.
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Jenő Hunyady (April 28, 1838 in Pest - December 26, 1889 in Budapest) was a Hungarian mathematician noted for his work on conic sections and linear algebra, specifically on determinants. He received his Ph.D. in Göttingen (1864). He worked at the University of Technology of Budapest. He was elected a corresponding member (1867), member (1883) of the Hungarian Academy of Sciences.
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Using the Dandelin spheres, it can be proved that any conic section is the locus of points for which the distance from a point (focus) is proportional to the distance from the directrix.Brannan, A. et al. Geometry, page 19 (Cambridge University Press, 1999). Ancient Greek mathematicians such as Pappus of Alexandria were aware of this property, but the Dandelin spheres facilitate the proof.
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The shell has a broadly elongate-conic shape. The shell reaches a length of 6.4 mm. The posterior third of the exposed portion of the whorls on the spire and a narrow area about the umbilical region are flesh- colored, while the rest of the shell is light chestnut brown. The 2½ whorls of the protoconch are small and smooth.
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The gills of the mushroom are closely spaced and white. The caps of L. decorosa, initially conic or hemispherical in shape, later expand to become convex or flattened in maturity. The caps are typically between in diameter, with surfaces covered with many small curved brown scales. The edge of the cap is typically curved inwards and may have coarse brown fibers attached.
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The flowering "cones" with paleae 9–15 mm long, with the ends red to orange-tipped, usually straight, and prickly-pointed. Ray flower corollas are purple or rarely pink or white. Discs or cones are ovoid to conic and 25–35 wide and 20–40 mm tall. Disc corollas 4.5–5.5 mm long with lobes greenish to pink or purple.
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Rahman, 2009) using the zig-zag construction of MacPherson-Vilonen (R. MacPherson & K. Vilonen, 1986). This perverse sheaf proved the Hübsch conjecture for isolated conic singularities, satisfied Poincarè duality, and aligned with some of the properties of the Kähler package. Satisfaction of all of the Kähler package by this Perverse sheaf for higher codimension strata is still an open problem.
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The very slender shell has an elongate-conic shape. Its length measures 8.3 mm. Its color is wax-yellow with a broad, brown band that on the early and the later whorls extends over the anterior half, between the sutures, while on the middle whorls it covers fully two-thirds of that space. The whorls of the protoconch are decollated.
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P. gilae is a small snail that has a height of and an ovate-conic, medium to large-sized shell. Its differentiated from other Pyrgulopsis in that its penial filament has a medium-length lobe and medium-length filament with the penial ornament consisting of two elongate penial glands, several other small dorsal glands; and curved, transverse terminal and ventral gland.
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Koreozospeum has a thin, squat ovate-conic shell, which shows fine spiral rows of interconnected pits constant throughout the teleoconch. The peristome has an oblique, ear-shaped (auriform) form. The shell shows a conspicuously pleated lip folded back onto the body whorl. Koreozospeum has an interrupted lamellar ridge on the next to last whorl, which then develops a uniformly shaped annular lamella.
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Fleischer rings are pigmented rings in the peripheral cornea, resulting from iron deposition in basal epithelial cells, in the form of hemosiderin. They are usually yellowish to dark-brown, and may be complete or broken. They are named for Bruno Fleischer. Fleischer rings are indicative of keratoconus, a degenerative corneal condition that causes the cornea to thin and change to a conic shape.
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In mathematics, the rational normal curve is a smooth, rational curve of degree in projective n-space . It is a simple example of a projective variety; formally, it is the Veronese variety when the domain is the projective line. For it is the plane conic and for it is the twisted cubic. The term "normal" refers to projective normality, not normal schemes.
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The colour of the shell is white. The spire is elevated conic, turriculate, nearly 1½ times the height of the aperture. The protoconch is globular, of 1½ smooth whorls, the nucleus broadly rounded. The shell contains 6 whorls, regularly increasing, with a high sloping shoulder, the keel on the spire-whorls near the middle, flat above and below the keel.
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The spiric sections result from the intersection of a torus with a plane that is parallel to the rotational symmetry axis of the torus. Consequently, spiric sections are fourth-order (quartic) plane curves, whereas the conic sections are second-order (quadratic) plane curves. Spiric sections are a special case of a toric section, and were the first toric sections to be described.
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The cones are conic, cylindrical or ovoid (egg-shaped), and small to very large, from 2–60 cm long and 1–20 cm broad. After ripening, the opening of non-serotinous pine cones is associated with their moisture content—cones are open when dry and closed when wet.Dawson, Colin; Vincent, Julian F. V.; Rocca, Anne-Marie. 1997. How pine cones open.
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The elongate-conic shell is vitreous. It measures 2.8 mm. The whorls of the protoconch are small, smooth, and almost completely obliquely immersed in the first of the succeeding turns, above which only the tilted edge of the last volution projects. The six whorls of the teleoconch are flattened, strongly contracted at the sutures and moderately shouldered at the summit.
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The elongate-conic shell is, subdiaphanous to milk-white. Its length measures 2.5 mm. The whorls of the protoconch are deeply obliquely immersed in the first of the succeeding: turns, above which only the tilted edge of the last one project. The six whorls of the teleoconch are somewhat contracted at the periphery and very strongly slopingly shouldered at the summit.
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The white shell has a broadly conic shape. Its length measures 3.3 mm. The whorls of the protoconch are smooth, almost completely obliquely immersed in the first of the succeeding turns, above which the tilted edge of the last whorl only projects. The seven whorls of the teleoconch are flattened, strongly contracted at the sutures and somewhat shouldered at the summit.
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Genus Achatinella Swainson, 1828: The dextral or sinistral shell is imperforate or minutely perforate, oblong, ovate or globose-conic; smooth or longitudinally corrugated, with only weak traces of spiral sculpture. Shell color is in spiral bands or streaks in the direction of the growth lines. The lip is simple or thickened within and sometimes slightly expanding. The columella bears a strong callous fold.
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The yellowish-white shell is broadly conic. Its length measures 4.4 mm. The protoconch is small with two whorls which increase extremely rapidly in size and are obliquely placed. The six whorls of the teleoconch are very strongly shouldered, marked by three very strong lamellar spiral keels on the first and second and four on the succeeding whorls between the sutures.
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The small shell is elongate-conic and translucent to milk-white. It measures 4 mm. The nuclear whorls are small and deeply immersed in the first of the succeeding turns, above which only a portion of the last turn is visible. The six post-nuclear whorls are moderately rounded, very weakly roundly shouldered at the summit and separated by a strongly marked suture.
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The elongate-conic shell is vitreous. It measures 2.3 mm. The nuclear whorls are obliquely immersed in the first post-nuclear turn, above which only the tilted edge of the last volution projects, which is marked by five slender spiral threads. The five post-nuclear whorls are well rounded, moderately contracted at the sutures, strongly slopingly shouldered at the summit.
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The regularly conic, yellowish white shell is umbilicated. It measures 4 mm. The whorls of the protoconch are apparently planorboid, very obliquely, almost completely, immersed in the first of the later whorls, only a portion of the last volution being visible. The six whorls of the teleoconch are rather high between the sutures, slightly rounded (almost flattened), and subtabulately shouldered at the summits.
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The milk-white shell is elongate, conic and turreted. Its length measures 2 mm. The whorls of the protoconch are deeply obliquely immersed in the first of the succeeding turns, above which only the tilted edge of the last volution projects. The six whorls of the teleoconch are strongly tabulately shouldered at the summit, flat in the middle, sloping suddenly toward the suture.
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The shell has an elongate-conic shape. Its length measures 11.5 mm. Its color is light wax yellow, with a supra and subperipheral light chestnut band, separated by a very narrow, dark wax yellow peripheral zone. (The whorls of the protoconch and probably the first two whorls of the teleoconch are decollated.) The nine remaining whorls are situated rather high between the sutures.
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The very slender shell has an elongate conic shape. The length of the type specimen measures 5.9 mm. Its color is light horn yellow with the anterior half of the base and a narrow, pale brown band about one-fifth of the width of the space between the sutures. The band is situated about its own width posterior to the periphery.
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The pale yellow shell has an elongate-conic shape. (The whorls of the protoconch are decollated). The five to seven whorls of the teleoconch are flattened in the middle between the sutures, strongly contracted at the periphery, moderately roundly shouldered at the summit. They are marked by rather strong lines of growth and exceedingly fine, closely spaced, microscopic spiral striations.
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The white shell has a medium size and is broadly conic. Its length measures 6.4 mm. The whorls of the protoconch number at least two. They form a depressed spire, the axis of which is almost at a right angle to the axis of the later whorls, and which is deeply, somewhat obliquely immersed in the first turn of the teleoconch .
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Bopp studied at the University of Strasbourg and the University of Heidelberg under Moritz Cantor. In 1906 he habilitated with a work about the conic sections of Grégoire de Saint-Vincent, and in 1915 he became professor extraordinarius in Heidelberg. As successor of Moritz Cantor he taught history of mathematics, political arithmetic, and Insurance. In 1933 he became ill and died in 1934.
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Sir Isaac Newton showed that a body controlled by the Sun moves in a conic section—that is, an ellipse, a parabola or a hyperbola. Because the latter two are open curves, a comet which pursued such a path would go off into space never to reappear. A derangement of orbit from closed to open curve has doubtless happened often.
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The most characteristic product of Greek mathematics may be the theory of conic sections, which was largely developed in the Hellenistic period. The methods used made no explicit use of algebra, nor trigonometry. Eudoxus of Cnidus developed a theory of real numbers strikingly similar to the modern theory of the Dedekind cut, developed by Richard Dedekind, who acknowledged Eudoxus as inspiration.
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In presentation of conic sections, de Witt sought kinematic motivation, independent of cross sections of a cone. Johannes Kepler, for example, had used kinematic geometric constructions. From 1647 to 1650 de Witt did legal work in The Hague and composed Elementa Curvarum Linearum, Liber Secundus, when he had the chance. In 1658 the Liber Primus was submitted to Frans van Schooten to introduce Liber Secundus.
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The interstices between the spirals are of about equal width as the cords, but that below the first spiral is slightly deeper and broader than the others. On the body whorl there are about 15 spirals, of which the lowest 6 are smooth. The colour of the shell is white. The spire has an elevated conic shape, the outlines somewhat convex, but little higher than the aperture.
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Felix Klein saw screw theory as an application of elliptic geometry and his Erlangen Program.Felix Klein (1902) (D.H. Delphenich translator) On Sir Robert Ball's Theory of Screws He also worked out elliptic geometry, and a fresh view of Euclidean geometry, with the Cayley–Klein metric. The use of a symmetric matrix for a von Staudt conic and metric, applied to screws, has been described by Harvey Lipkin.
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Segre's theorem states that in a Galois geometry of odd order (that is, a projective plane defined over a finite field of odd characteristic) every oval is a conic. This result is often credited with establishing Galois geometries as a significant area of research. At the 1958 International Mathematical Congress Segre presented a survey of results in Galois geometry known up to that time.
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The whitish to creamy white gills are waxy in appearance and consistency. The cap of M. flavoalba is in diameter, conical when young, becoming somewhat bell-shaped, broadly conic or at times nearly convex. It may develop a papilla (a nipple-like structure) in its center. The cap margin is initially pressed against the stem, but in maturity either flares out or curves inward slightly.
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The shell size varies between 20 mm and 45 mm, with the average size ranging from 35 mm to 40 mm. Usually the shell has dark brown ribs and orange background, but there are several different variations of color. It is an active hunter of other molluscs, feeding on snails, slugs, mussels and clams. The ovate, bi-conic shell is quite thick and solid.
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The shell has a turbinate-conic shape as in Euchelus. The spire is elevated. The operculum is multispiral as in a typical Trochus and with more, less rapidly expanding whorls compared with Euchelus.Tryon (1889), Manual of Conchology XI, Academy of Natural Sciences, Philadelphia Species in this genus has typically two teeth, joined by a U-shaped notch, where the columella and the basal lips join.
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On an Earth-to-Mars transfer, a hyperbolic trajectory is required to escape from Earth's gravity well, then an elliptic or hyperbolic trajectory in the Sun's sphere of influence is required to transfer from Earth's sphere of influence to that of Mars, etc. By patching these conic sections together—matching the position and velocity vectors between segments—the appropriate mission trajectory can be found.
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The milk-white shell has an elongate-conic shape. The length of the shell measures 3.6 mm. The 2¾ whorls of the protoconch form a decidedly elevated helicoid spire, the axis of which is at right angles to that of the succeeding turns, in the first of which they are about one-fourth immersed. A complete shell would probably have twelve whorls in the teleoconch.
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The thin, semitranslucent shell has an elongate-conic shape. Its length measures 3 mm. The whorls of the protoconch are obliquely immersed in the first of the succeeding turns, above which only the tilted edge of the last volution projects, which is marked by three strongly elevated spiral threads. The six whorls of the protoconch are well-rounded, moderately contracted at the sutures, and strongly slopingly shouldered.
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The height of the shell attains 8 mm. The imperforate, dull white shell has an ovate-conic, subventricose shape. The apex rather obtuse. The shell is ornamented with strong spiral subnodose ribs, decussated by elevated rib-striae cutting the interstices into square pits, of which there are 3 or 4 series on the third whorl, 4 on the penultimate, and 7 on the last.
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The height of the shell varies between 10 mm and 12 mm, its diameter between 12 mm and 15 mm. The very solid, deeply, narrowly false- umbilicate shell has a globose-conic shape. It is fawn colored, lighter beneath and roseate at the apex. The shell is sharply granose-lirate, usually with every second rib articulated with dots of white or black or both.
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The flowers are light green with reddy-brown spots. Sepals are similar, usually concave, oblong-elliptic, 4.5-5 × 2.5–3 mm, apex obtuse. Petals are somewhat obovate, slightly smaller than sepals, tip blunt, lip with an epichile and a saccate hypochile. Epichile is nearly suborbicular, about 3 × 5 mm, adaxially hairless, with a central cushion, near base with 2 conic calli, entire, obtuse at apex.
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There is a considerable morphological variation in this so-called pollen presenter between species. The pollen presenter may be cylindric, oval, or conic in shape, either or not split in two lobes near the tip or oblique. The very tip has a groove that functions as the stigma that is centrally or oblique oriented. The finely powdery ovary is long, and gradually merges into the style base.
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Isaac Newton developed a convenient and inexpensive sundial, in which a small mirror is placed on the sill of a south- facing window.Waugh (1973), pp. 116–121. The mirror acts like a nodus, casting a single spot of light on the ceiling. Depending on the geographical latitude and time of year, the light-spot follows a conic section, such as the hyperbolae of the pelikonon.
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The shell is very small, its length measuring 3.5 – 4 mm and it is 6.5 mm wide. The small, very solid, shell has an depressed, orbicular shape with a conic spire. The 4½-5 whorls are convex and strongly spirally lirate.These lirae are smooth, about twelve in number on the body whorl, three on penultimate whorl, not perceptibly crenulated by the very subtle incremental stride.
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The milk-white shell has a regularly elongate-conic shape. It measures 6.7 mm. The whorls of the protoconch are small, obliquely almost completely immersed in the first of the succeeding whorls, only the periphery of the last two being visible. The nine whorls of the teleoconch are rather high between the sutures, very slightly rounded, slightly angulated at the periphery and scarcely at all shouldered.
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The stout, rough shell has a very broadly conic shape and is narrowly umbilicated. Its length measures 8 mm. The whorls of the protoconch are small, deeply obliquely immersed in the first turn of the teleoconch. The seven whorls of the teleoconch are with quite strong concavely shouldered summits, the rest well rounded (usually showing decided erosion marks which coincide largely with the lines of growth).
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The size of the shell varies between 6 mm and 16 mm. The shell has a depressed conic shape with a rather acute apex and six whorls. The nucleus is white and delicately sculptured. The remainder of the shell is whitish with faint streaks of brown transverse to the whorls, arranged so as to present the appearance of seven brownish streaks radiating from the apex.
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Cone with cross-sections The diagram represents a cone with its axis . The point A is its apex. An inclined cross-section of the cone, shown in pink, is inclined from the axis by the same angle , as the side of the cone. According to the definition of a parabola as a conic section, the boundary of this pink cross- section EPD is a parabola.
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Suture is very oblique, ascending to the aperture. Aperture is quite obliquely piriform, excised by the very oblique parietal wall. Aperture has 4 teeth: 1 parietal lamella, 1 conic tooth at the lower end of the sharply emerging, dark-colored columella; 2 short, widely separated, deeply immersed palatal folds. Margins are delicately united, the outer margin is weakly arcuate, nearly straight, the columellar margin is broadly reflected.
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A sectional chart is a two-sided chart created from a Lambert Conformal Conic Projection with two defined standard parallels. The scale is 1:500,000, with a contour interval of 500 feet. The size of each sectional is designed to be "arm's width" when completely unfolded. The "northern" half of the section is on one side of the chart, and the "southern" on the reverse.
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The yellowish white shell has a very regularly, and broadly elongate conic shape. Its length measures 4.2 mm. The 2¾ clear and smooth whorls of the protoconch are strongly rounded. They form a strongly elevated spire having its axis at right angles to that of the succeeding turns, in the first of which the side of the last revolution is about one-fifth immersed.
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The shell has an elongate conic shape. Its length measures 6.8 mm. The shell is flesh colored, excepting a broad chestnut band which covers the median third of the last whorl. This dark band really consists of two chestnut-colored zones, the anterior of which embraces half of the band while the posterior is equal to one-fourth of the width of the dark area.
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The spire is conic. The five whorls are a little tumid below each suture, and with a narrow ledge or margin, marked off by an impressed line, above each suture. This peripheral ledge gives the body whorl a rather prominent keel. The surface is polished, but shows quite prominent, spaced, impressed growth lines, and under a lens is all over very densely minutely spirally striate.
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The shell of an adult Gibbula ardens can be as large as . The solid, umbilicate shell has a depressed conic shape with a variable sculpture. Its color is quite variable, but usually is reddish or olive brown, with a subsutural series of short white flammules, a row of white spots on the periphery, the remainder of the surface sparsely punctate with white. The spire is acute.
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The milk-white shell has an elongate-conic shape. Its length measures 2.3 mm. The three whorls of the protoconch form an elevated helicoid spire, whose axis is at right angles to that of the succeeding turns, in the first of which it is almost half immersed. The seven whorls of the teleoconch are moderately rounded, somewhat contracted at the suture, and strongly shouldered at the summit.
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The two arms are smoothly connected at the pole. Taking the mirror image of one arm across the 90°/270° line will yield the other arm. This curve is notable as one of the first curves, after the conic sections, to be described in a mathematical treatise, and as being a prime example of a curve that is best defined by a polar equation.
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Toomer, p. 24. Fragments of a work by Diocles entitled On burning mirrors were preserved by Eutocius in his commentary of Archimedes' On the Sphere and the Cylinder. Historically, On burning mirrors had a large influence on Arabic mathematicians, particularly on al-Haytham, the 11th- century polymath of Cairo whom Europeans knew as "Alhazen". The treatise contains sixteen propositions that are proved by conic sections.
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The Steiner inellipse plays a special role: Its area is the greatest of all inellipses. Because a non-degenerate conic section is uniquely determined by five items out of the sets of vertices and tangents, in a triangle whose three sides are given as tangents one can specify only the points of contact on two sides. The third point of contact is then uniquely determined.
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The large shell is white and has an elongate-conic shape. Its length measures 5.1 mm. The whorls of the protoconch are smooth, deeply obliquely immersed in the first of the succeeding turns, above which only a portion of the last volution projects. The eight whorls of the teleoconch are very slightly rounded, moderately contracted at the sutures, slightly excurved at the shouldered summit.
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The word asymptote is derived from the Greek ἀσύμπτωτος (asumptōtos) which means "not falling together", from ἀ priv. + σύν "together" + πτωτ-ός "fallen".Oxford English Dictionary, second edition, 1989. The term was introduced by Apollonius of Perga in his work on conic sections, but in contrast to its modern meaning, he used it to mean any line that does not intersect the given curve.
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The shell in non-crowded specimens of Chamaesipho brunnea is usually low conic, brown with prominent growth ridges basally, corroded upper sections are whiter and smoother. Crowded individuals become columnar. Shell wall in juveniles, to 4 mm maximum diameter consists of six plates, which then reduce to four by fusion of carinolatera with rostrolatera. Complete fusion of wall is accomplished by reproductive maturity, 5–6 mm diameter.
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Psilocybe strictipes has a farinaceous smell and taste. Pleurocystidia are absent and its lageniform cheilocystidia are 21-45 by 7-10 µm. The cap is 5 to 30 mm across, conic to campanulate to convex, smooth, and translucent-striate near the margin, often with a low umbo. It is walnut brown to dark rusty brown, with a smooth surface and a separable gelatinous pellicle.
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All of the species in this genus have thick-walled high-spired shells, and some attain a length of over 4 cm. The shape of the shell is elongate-conic or cylindrical. The sculpture of the shell is often carinate or costate. The shell of larger species sometimes develops sculpturing and a small siphonal canal or siphonal notch at the base of the aperture.
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Several modern authors still consider non-Euclidean geometry and hyperbolic geometry synonyms. Arthur Cayley noted that distance between points inside a conic could be defined in terms of logarithm and the projective cross-ratio function. The method has become called the Cayley–Klein metric because Felix Klein exploited it to describe the non-Euclidean geometries in articlesF. Klein, Über die sogenannte nichteuklidische Geometrie, Mathematische Annalen, 4(1871).
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In the 3D space, the circle parameters can be identified by the intersection of many conic surfaces that are defined by points on the 2D circle. This process can be divided into two stages. The first stage is fixing radius then find the optimal center of circles in a 2D parameter space. The second stage is to find the optimal radius in a one dimensional parameter space.
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Another concrete realization would be obtained by thinking of as the 3×3 symmetric matrix which represents it. If and have such concrete realizations then every member of the above pencil will as well. Since the setting uses homogeneous coordinates in a projective plane, two concrete representations (either equations or matrices) give the same conic if they differ by a non-zero multiplicative constant.
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The milk-white shell has a regularly conic shape. Its length measures 3.6 mm. The whorls of the protoconch are very obliquely deeply immersed in the first of the succeeding turns, above which only the tilted edge of the last volution projects, which gives the spire a decidedly truncated aspect. The six whorls of the teleoconch are well rounded, slightly shouldered at the summit.
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The yellowish-white shell measures 10.2 mm and is one of the largest in this genus. It is very thin, broadly conic, umbilicated. It is marked by subobsolete, subequal, and subequally spaced spiral wrinkles, about fifteen of which may be seen on the body and base of the body whorl. In addition to these wrinkles, many faint, closely placed spiral and vertical grooves are present.
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The elongate-conic shell is milk-white. Its length is 3.2 mm. The seven whorls of the teleoconch are very slightly rounded, somewhat contracted at the sutures, feebly shouldered at the summits. They are marked by strong, almost vertical axial ribs, of which 14 occur upon the second, 16 upon the third, 18 upon the fourth, 20 upon the fifth, and 22 upon the penultimate turn.
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Most Teleuts used to be nomadic or semi-nomadic livestock herders and horses, goats, cattle, and sheep were the most common types of animals they raised. Some Teleuts were hunters and relied on animals living in the taiga for subsistence. Traditional Teleut dwellings included conic yurts made out of bark or perches. Common Teleut dress was composed of linen shirts, short breeches, and single-breasted robes.
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The elongate-conic shell is white. It measures 4.8 mm. The whorls of the protoconch are small, deeply obliquely immersed in the first post-nuclear turn, above which only the tilted edge of the last volution projects. The six whorls of the teleoconch are well rounded, marked by slender, nodulous, retractive axial ribs, wliich terminate at the posterior extremity of the supra-peripheral cord, leaving this smooth.
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The elongate-conic shell is vitreous and translucent. Its length measures 2.3 mm. The whorls of the protoconch are deeply obliquely immersed in the first of the succeeding turns, above which only the tilted edge of the last volution projects. The six whorls of the teleoconch are flattened, very strongly angulated at the periphery where they are much wider than at the appressed summit.
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The elongate-conic, slender shell is vitreous. It measures 2.5 mm. The two and one-half nuclear whorls form a depressed helicoid spire, whose axis is almost at right angles to that of the succeeding turns, in the first of which it is about one-half immersed. The seven post-nuclear whorls are very slightly rounded, strongly constricted at the sutures and prominently shouldered at the summit.
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Dmitrii Matveevich Sintsov (21 November 1867, in Vyatka – 28 January 1946) was a Russian mathematician known for his work in the theory of conic sections and non-holonomic geometry. He took a leading role in the development of mathematics at the University of Kharkiv, serving as chairman of the Kharkov Mathematical Society for forty years, from 1906 until his death at the age of 78.
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The robust dull brown shell is large and broadly conic. (The whorls of the protoconch are decollated and probably the first whorl of teleoconch is missing from the type specimen) All but the last whorl of the teleoconch are flattened, flatly shouldered and crenulated at the summit. The body whorl is inflated and well rounded. The periphery of the body whorl is marked by a strong sulcus.
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The small, white shell has a broadly conic shape. Its length measures 3 mm. The three whorls of the protoconch form a depressed helicoid spire, whose axis is at right angles to that of the succeeding turns, in the first of which it is about one-third immersed. The 5½ whorls of the teleoconch are strongly rounded, moderately contracted at the suture, broadly tabulated at the shoulder.
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The very small, bluish-white shell is very regularly narrowly conic. The shell grows to a length of 3.1 mm. The whorls of the protoconch are deeply obliquely immersed in the first of the succeeding turns, above which only the tilted edge of the last volution projects. The whorls of the teleoconch are slightly rounded, feebly contracted at the sutures, and very narrowly shouldered at the summit.
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3 Desargues developed an alternative way of constructing perspective drawings by generalizing the use of vanishing points to include the case when these are infinitely far away. He made Euclidean geometry, where parallel lines are truly parallel, into a special case of an all-encompassing geometric system. Desargues's study on conic sections drew the attention of 16-year-old Blaise Pascal and helped him formulate Pascal's theorem.
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A point has a solid construction if it can be constructed using a straightedge, compass, and a (possibly hypothetical) conic drawing tool that can draw any conic with already constructed focus, directrix, and eccentricity. The same set of points can often be constructed using a smaller set of tools. For example, using a compass, straightedge, and a piece of paper on which we have the parabola y=x2 together with the points (0,0) and (1,0), one can construct any complex number that has a solid construction. Likewise, a tool that can draw any ellipse with already constructed foci and major axis (think two pins and a piece of string) is just as powerful.P. Hummel, "Solid constructions using ellipses", The Pi Mu Epsilon Journal, 11(8), 429 -- 435 (2003) The ancient Greeks knew that doubling the cube and trisecting an arbitrary angle both had solid constructions.
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The degenerate conic is either: a point, when the plane intersects the cone only at the apex; a straight line, when the plane is tangent to the cone (it contains exactly one generator of the cone); or a pair of intersecting lines (two generators of the cone). These correspond respectively to the limiting forms of an ellipse, parabola, and a hyperbola. If a conic in the Euclidean plane is being defined by the zeros of a quadratic equation (that is, as a quadric), then the degenerate conics are: the empty set, a point, or a pair of lines which may be parallel, intersect at a point, or coincide. The empty set case may correspond either to a pair of complex conjugate parallel lines such as with the equation x^2+1=0, or to an imaginary ellipse, such as with the equation x^2 +y^2+1=0.
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Small-scale DLGs are sold in state units and are cast on either the Albers equal-area conic projection system or the geographic coordinate system of latitude and longitude, depending on the distribution format. All DLGs are referenced to the North American Datum of 1927 (NAD27) or the North American Datum of 1983 (NAD83). USGS DLGs are topologically structured for use in mapping and geographic information system (GIS) applications.
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Although successful in solving Apollonius' problem, van Roomen's method has a drawback. A prized property in classical Euclidean geometry is the ability to solve problems using only a compass and a straightedge. Many constructions are impossible using only these tools, such as dividing an angle in three equal parts. However, many such "impossible" problems can be solved by intersecting curves such as hyperbolas, ellipses and parabolas (conic sections).
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Some remote regions, where Greeks and Romans mostly explored and traded rather than settled (i.e. Baltic, Arabia, East Africa, India, Sri Lanka), are of the scale 1:5,000,000. Due to the nature of the base maps used for the background and time–cost restrictions, elevation lines (contours) were left in feet except for the 1:150,000 maps where they are in meters. The projection of the maps is Lambert Conformal Conic.
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The gills are interspersed with two or three tiers of short gills. The cap initially has a sharply conic shape, but expands to a narrow bell-shape or a broad cone in maturity, typically reaching in diameter. The cap margin, which is initially pressed against the stem, is opaque or nearly so at first. It is scarlet red when fresh and moist, becoming orange or yellowish orange before losing moisture.
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The length of the shell attains 28 mm, its diameter 6.7 mm. (Original description) The very elongate- conic shell is bluish white. The protoconch contains 2.5 whorls, the first two well rounded, smooth, the last half crossed by a number of distantly spaced axial riblets. The postnuclear whorls are well rounded, the first with two nodulose spiral threads, the second with three, of which the median is the strongest.
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Osculating orbit (inner, black) and perturbed orbit (red) In astronomy, and in particular in astrodynamics, the osculating orbit of an object in space at a given moment in time is the gravitational Kepler orbit (i.e. an elliptic or other conic one) that it would have around its central body if perturbations were absent. That is, it is the orbit that coincides with the current orbital state vectors (position and velocity).
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They have slender holes making the tops of the towers light and elegant reminiscent of the conic formation of the chestnut flowers one can find blooming in trees along the walkways in the Vyšehrad complex. The spires (and indeed the triangular gable of the façade between them) are frilled with pedal like finial protrusions along their length and on their tops, further connecting their likeness to the flower.
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The slender shell is elongate-conic, semitranslucent and shining. It measures 3.6 mm. The nuclear whorls are moderately large, almost completely obliquely immersed in the first of the succeeding whorls; the peripheral edge only of the last volution is visible above this. The six post-nuclear whorls are situated rather high between the sutures, slightly rounded (almost flattened), faintly shouldered at the summit, apparently without axial or spiral sculpture.
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Let ABCDEF be a hexagon formed by six tangent lines of a conic section. Then Brianchon's theorem states that the three main diagonals AD, BE, and CF intersect at a single point. In a hexagon that is tangential to a circle and that has consecutive sides a, b, c, d, e, and f,Gutierrez, Antonio, "Hexagon, Inscribed Circle, Tangent, Semiperimeter", , Accessed 2012-04-17. :a+c+e=b+d+f.
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The pale yellowish brown shell is rather large (compared to the other species in this genus) and has an elongate conic shape. Its length measures 6.5 mm. The 2½ whorls of the protoconch are well rounded. They form a decidedly depressed helicoid spire, the axis of which is at right angles to that of the succeeding turns in the first of which the tilted edge is about one-fifth immersed.
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The discriminant of the conic section's quadratic equation (or equivalently the determinant of the 2×2 matrix) and the quantity (the trace of the 2×2 matrix) are invariant under arbitrary rotations and translations of the coordinate axes,Pettofrezzo, Anthony, Matrices and Transformations, Dover Publ., 1966, p. 110. as is the determinant of the 3×3 matrix above. The constant term and the sum are invariant under rotation only.
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Three barnacles of Notochthamalus scabrosus (the one on the bottom left is of the genus Jehlius) Notochthamalus is composed of 6 compartmental plates, composed of a carina, rostrum, and paired carinolatera and rostrolatera. Sutures between plates made up of poorly developed oblique folded laminae with membraneous basis. Plates are colored dull purplish brown, weathering to gray. Free-growing shellis are conic, crowded colonies become cylindrical, with plate sutures obscured.
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Campo & Papadopoulos (2014) Cayley–Klein geometry is the study of the group of motions that leave the Cayley–Klein metric invariant. It depends upon the selection of a quadric or conic that becomes the absolute of the space. This group is obtained as the collineations for which the absolute is stable. Indeed, cross-ratio is invariant under any collineation, and the stable absolute enables the metric comparison, which will be equality.
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It weighs 134 grams. The North-South axis is vertical reflecting the thinking of Aristotle. Its twin, the Lenox Globe (at the New York Public Library), is a cast made of red copper representing the Earth in the center of an armillary sphere. The Ostrich Egg Globe depicts numerous subjects, including ships, a volcano, sailors, a monster, ocean waves, conic mountains, rivers, coastal lines, and a triangular anagram.
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Apollonius of Perga reported that Conon worked on conic sections, and his work became the basis for Apollonius' fourth book of the Conics. Apollonius further reports that Conon sent some of his work to Thrasydaeus, but that it was incorrect. Since this work has not survived it is impossible to assess the accuracy of Apollonius' comment. In astronomy, Conon wrote in seven books his De astrologia, including observations on solar eclipses.
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By that time she had studied plane and spherical trigonometry, conic sections and James Ferguson's Astronomy. Now she first read Isaac Newton's Principia, which she continued to study. Her inheritance from Greig gave her the freedom to pursue intellectual interests. John Playfair, professor of natural philosophy at University of Edinburgh, encouraged her studies, and through him she began a correspondence with William Wallace, with whom she discussed mathematical problems.
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The surface of the shell is finely spirally striate, the striae about 8 on the body whorl, with a couple of stronger ribs at the periphery, which are visible above the suture on the spire whorls. The short spire is conic, acute, with its lateral outlines rectilinear. The 7–8 whorls are flat, the last one acutely carinated, and flat beneath. The oblique aperture is rhomboidal, smooth and nacreous within.
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The milk-white shell has a broadly elongate-conic shape, very regularly tapering and is subturrited. The type specimen measures 5 mm. The 2½ whorls of the protoconch are small, helicoid, well rounded, moderately elevated, about one-third immersed in the first of the later whorls, having their axis almost at a right angle to them. The seven whorls of the teleoconch are rather high between the sutures.
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Pierre Dangicourt (1664 Rouen - 12 Feb 1727 Berlin) was a French mathematician. As a Protestant, he left France after the Edict of Fontainebleau and settled in Prussia, where he was made an associate member of the Academy of Berlin. Dangicourt became a student and friend of Gottfried Leibniz, and the two shared a long correspondence. Dangicourt's publications include works on conic sections and on the binary number system invented by Leibniz.
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The term "waveguide" is used to describe horns with low acoustic loading, such as conic, quadratic, oblate spheroidal or elliptic cylindrical horns. These are designed more to control the radiation pattern rather than to gain efficiency via improved acoustic loading. All horns have some pattern control, and all waveguides provide a degree of acoustic loading, so the difference between a waveguide and a horn is a matter of judgement.
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'Stayman' is a medium-sized, roundish-conic apple with a thick, greenish-yellow skin covered almost entirely with a deep red blush, darker red stripes, and russet dots. The stem cavity often shows heavy russetting. Firm, tender, finely textured, juicy, crisp, and yellowish-green, the flesh is tart and spicy. They keep very well, and are used primarily as dessert apples, but also make a fine addition to blended cider.
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The size of the shell attains 17 mm. The thick, solid shell has a depressed conoidalshape. It is of a reddish-brown hue, interstices between the ribs, chocolate colored, above marked with a few broad yellowish or flesh-tinted maculations radiating from the sutures toward, but not quite reaching the periphery, which with the base, has the ribs sparsely dotted with white. The spire is low-conic with a roseate apex.
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The height of the shell varies between 10 mm and 20 mm. The pointed, imperforate, solid shell has an elongated conic shape. It is polished, yellowish, pink, or olive-green, with reddish or olive longitudinal lines in pairs, sometimes separate on the body whorl, and usually with numerous narrow, rather obscure spiral pink or yellowish lines. It sometimes has a few series of white dots on the upper part.
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The shell is large and has an elongate-conic shape. The length of the type specimen measures 9.9 mm (with the protoconch decollated as well as probably the first turn). The shell is yellowish-white, with a light-brown area about the columella. (Nuclear whorls decollated.) The 13 remaining whorls of the teleoconch are well rounded, slightly shouldered at the summit and scarcely at all contracted at the periphery.
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Reconstruction of a house in Sanfins The Citânia was protected by three lines of walls, with an exterior wall protecting the West and South and a moat in the North and South. These walls were created using local granite blocks. About 160 houses have been found within the Citânia walls. Most of these houses are circular, with diameters of about 5m, granitic stone walls, and conic ceilings made of perishable materials.
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The milk-white shell is small and has an elongate-conic shape. Its length measures 4.1 mm. The 2½ whorls of the protoconch form a depressed, helicoid spire, whose axis is at right angles to that of the succeeding turns, in the first of which it is about one-fifth immersed. The nine whorls of the teleoconch are slightly rounded, appressed at the summit, and moderately contracted at the suture.
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Calocedrus decurrens is a large tree, typically reaching heights of and a trunk diameter of up to . The largest known tree, located in Klamath National Forest, Siskiyou County, California, is tall with a circumference trunk and a spread. It has a broad conic crown of spreading branches. The bark is orange-brown weathering grayish, smooth at first, becoming fissured and exfoliating in long strips on the lower trunk on old trees.
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This is equivalent to requiring unless . Right away, this explains why the choice of elementary solutions we made earlier worked so well: obviously will be solutions. Applying Fourier inversion to these delta functions, we obtain the elementary solutions we picked earlier. But from the higher point of view, one does not pick elementary solutions, but rather considers the space of all distributions which are supported on the (degenerate) conic .
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Each coordinate of the intersection points of two conic sections is a solution of a quartic equation. The same is true for the intersection of a line and a torus. It follows that quartic equations often arise in computational geometry and all related fields such as computer graphics, computer-aided design, computer-aided manufacturing and optics. Here are examples of other geometric problems whose solution involves solving a quartic equation.
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The proportionality is seen by the fact that the ratio for Jupiter, 5.23/11.862, is practically equal to that for Venus, 0.7233/0.6152, in accord with the relationship. Idealised orbits meeting these rules are known as Kepler orbits. The lines traced out by orbits dominated by the gravity of a central source are conic sections: the shapes of the curves of intersection between a plane and a cone.
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It keeps an amount of functionality of C.a.R. but uses a different graphical interface which purportedly eliminates some intermediate dialogs and provides direct access to numerous effects. Constructions are done using a main palette, which contains some useful construction shortcuts in addition to the standard compass and ruler tools. These include perpendicular bisector, circle through three points, circumcircular arc through three points, and conic section through five points.
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"Omar Al Hay of Chorassan, about 1079 AD did most to elevate to a method the solution of the algebraic equations by intersecting conics." It is divided into three parts: (i) equations which can be solved with compass and straight edge, (ii) equations which can be solved by means of conic sections, and (iii) equations which involve the inverse of the unknown.Bijan Vahabzadeh, "Khayyam, Omar xv. As Mathematician", Encyclopædia Iranica.
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The theorem was further generalized by Dao Thanh Oai. The generalization as follows: First generalization: Let ABC be a triangle, P be a point on the plane, let three parallel segments AA', BB', CC' such that its midpoints and P are collinear. Then PA', PB', PC' meet BC, CA, AB respectively at three collinear points. Dao's second generalization Second generalization: Let a conic S and a point P on the plane.
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The shell attains a size between 17 mm and 60 mm. The solid, imperforate shell has a conic shape. Its color pattern is olivaceous brown, maculated obscurely above with brown, green or white. The seven whorls are longitudinally costate below the sutures and above the periphery, with two spiral series of tubercles around the middle of the flattened upper surface, or sometimes finely irregularly plicate over the whole upper surface.
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Morin khuur vary in form depending on region. Instruments from central Mongolia tend to have larger bodies and thus possess more volume than the smaller-bodied instruments of Inner Mongolia. In addition, the Inner Mongolian instruments have mostly mechanics for tightening the strings, where Mongolian luthiers mostly use wooden pegs in a slightly conic shape. In Tuva, the morin khuur is sometimes used in place of the igil.
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The thin, yellowish white shell has a broadly elongate conic shape. The whorls of the protoconch are small, deeply embedded in the first of the succeeding turns, above which the tilted edge of the last volution only projects. The whorls of the teleoconch are inflated, well rounded, and feebly shouldered at the summit. They are marked by almost vertical, very feeble, incremental lines and exceedingly fine, closely spaced, spiral striations.
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The elongate-conic shell is of medium size, measuring 6.1 mm. It is yellowish-white, the exterior surface marked by irregular tumescences, giving it a much worn appearance. The three whorls of the protoconch are deeply immersed, having their axis at about a right angle to the axis of the succeeding turns. The six whorls of the teleoconch are moderately well rounded and faintly shouldered at the summit.
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The elongate-conic shell is semitranslucent and measures 5.8 mm. The whorls of the protoconch are small, forming a depressed helicoid spire, which is a little more than half obliquely immersed in the first of the succeeding turns. The eight whorls of the teleoconch are moderately rounded, marked by four strong, equal, and almost equally spaced spiral cords which are separated by three well-incised spiral grooves. The suture is subchanneled.
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This is a little brown mushroom that grows on dung and has black spores. It has a cap that is less than 4 cm across, hygrophanous, conic to campanulate to plane, usually with an umbo. The gills are dark purplish black, crowded, with several tiers of intermediate gills. The spores are (11) 13 - 15 (17) x 9 - 11 (12) x (6.5) 7 - 8 (9) micrometers, smooth, black, and shaped like lemons.
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The body whorl is not dilated at the periphery. The flat base is concentrically grooved. The columella is less oblique than in the type.Tryon (1889), Manual of Conchology XI, Academy of Natural Sciences, Philadelphia This species was first considered an arrested or primitive form of Tectus niloticus, as in the conic form, flat, lirate base, and sculptured spire, it exactly resembles an immature specimen of the latter species.
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They are usually created with the intention of generating a specific result not achievable using conic curves. At times they are created using combinations of definable curves but not always. Modern light tracing software can generate curves using impact angles to generate a point cloud to define a required shape. Aconic reflectors are used in ultra violet light UV curing devices to smooth light density for a more uniform curing pattern.
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The elongate-conic shell is milk-white. Its length is 4.8 mm. The whorls of the protoconch are deeply obliquely immersed in the first of the succeeding turns, above which only the edge of the last volution projects. The seven whorls of the teleoconch are flattened in the middle (in this, it differs from O. tenuis and O. valdesi), moderately contracted at the suture, and roundly shouldered at the summit.
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The bluish-white shell has a very elongate conic shape. Its length measures 3.3 mm. The two whorls of the protoconch are smooth, forming a depressed helicoid spire, whose axis is at right angles to that of the succeeding turns, in the first of which it is about half immersed. The eight whorls of the teleoconch are moderately rounded, slightly shouldered at the summit, somewhat contracted at the sutures.
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The robust shell is conic, ventricose, subcrystalline and has a straight spire. Its length measures 2.2 mm. The three whorls of the protoconch form an acute apex, having their axis at right angles to that of the succeeding turn. The four whorls of the teleoconch are marked by three broad, strong, somewhat rounded, spiral keels between the sutures, the spaces between which are less wide than the keels.
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On the body whorl they change their character, becoming mere striations, and more numerous than in the fasciole of the anal sinus. A second slightly gemmed thread appears on the body whorl, and 2 fine spiral lines on the anterior tabulation. On the base of the shell there are 4 strong spirals, and on the siphonal canal about 10 much weaker. The spireis conic, very little higher than the aperture.
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After approximately seven years, he left CONIC and helped form a new organization, Encuentro Campesino (Peasant Encounter/Gathering). Choc continued helping indigenous Q'eqchi' communities reclaim their rights, especially through Encuentro Campesino. Choc didn't only work with Q'eqchi' communities but also with Ladino (of Spanish or mixed descent) and Garifuna (of African descent) peasants. On February 14, 2008, Choc was illegally abducted by the military and threatened with assassination.
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The height of the shell attains 5 mm, its diameter 7 mm. The polished, smooth, thin but solid shell has a conic shape with a flat base. Its color pattern is dark purple, unicolored with a reddish apex, or with an opaque white band on the lower part of each whorl, or with the entire upper surface of the two outer whorls white, the base purple. The conical spire has straight lateral outlines.
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Using his version of a coordinate system, Apollonius manages to develop in pictorial form the geometric equivalents of the equations for the conic sections, which raises the question of whether his coordinate system can be considered Cartesian. There are some differences. The Cartesian system is to be regarded as universal, covering all figures in all space applied before any calculation is done. It has four quadrants divided by the two crossed axes.
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The shell grows to a length of 17 mm, its diameter 6.9 mm. (Original description) The elongate-conic shell is wax-yellow with a broad pale-brown band at the periphery. The protoconch contains 2.5 smooth whorls 2.5, forming a pointed apex. The beginning of the postnuclear whorls has the axial riblets characteristic of the later postnuclear whorls, but here they are a little more slender and a little more closely approximated.
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Alfred Stillé (October 30, 1813 – September 24, 1900) was an American physician. Born in Philadelphia, he studied classics at Yale, but was expelled for participating in the Conic Sections Rebellion. He then transferred to the University of Pennsylvania in the same year, where he received an A.B. degree in 1832. He went on to get an A.M. from the University of Pennsylvania in 1835 and in 1836 an M.D. from the school's department of medicine.
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The crown is conic, with widely spaced branches with drooping branchlets. The shoots are stout, pale buff-brown, glabrous, and with prominent pulvini. The leaves are needle-like, 17–23 mm long, stout, rhombic in cross-section, bright glaucous blue-green with conspicuous lines of stomata; the tip is viciously sharp. The cones are pendulous, broad cylindrical, 7–12 cm long and 3 cm broad when closed, opening to 4–5 cm broad.
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The crown is conic, with widely spaced branches with drooping branchlets. The shoots are stout, pale buff-brown, glabrous, and with prominent pulvini. The leaves are needle-like, 23–35 mm long, stout, moderately flattened in cross-section, bright glossy green with inconspicuous lines of stomata; the tip is viciously sharp. The cones are pendulous, broad cylindrical, 8–16 cm long and 3 cm broad when closed, opening to 6 cm broad.
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Incipit Zimmermann was born in Vaihingen, Württemberg (now Germany) on November 25, 1642."Who Do You Think You Are?", tracing lineage of Josh Groban back to his 8th grandfather, Johann Jacob Zimmermann He lived in Nürtingen, and studied theology at the University of Tübingen, where he was awarded the title Magister in 1664. An astronomer and astrologer, Zimmermann produced one of the first Equidistant Conic Projection star charts of the northern hemisphere in 1692.
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The milk-white shell is slender and has an elongate conic shape. Its length measures 8 mm. The 2½ whorls of the protoconch are well rounded, forming a moderately elevated spire, the axis of which is at right angles to that of the succeeding turns, in the first of which the tilted spire is one-fifth immersed. The type specimen has 12 or 13 (the first is probably lost) whorls in the teleoconch.
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A projective cone (or just cone) in projective geometry is the union of all lines that intersect a projective subspace R (the apex of the cone) and an arbitrary subset A (the basis) of some other subspace S, disjoint from R. In the special case that R is a single point, S is a plane, and A is a conic section on S, the projective cone is a conical surface; hence the name.
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The rather stout, milk-white shell has an elongate-conic shape. Its length measures 5.1 mm. The two whorls of the protoconch form a planorboid spire, whose axis is at right angles to the succeeding turns, in the first of which it is about one-fourth immersed. The nine whorls of the teleoconch are flattened in the middle, with a strongly sloping shoulder which extends over the posterior fourth between the sutures.
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Karl Georg Christian von Staudt defined a conic as the point set given by all the absolute points of a polarity that has absolute points. Von Staudt introduced this definition in Geometrie der Lage (1847) as part of his attempt to remove all metrical concepts from projective geometry. A polarity, , of a projective plane, , is an involutory (i.e., of order two) bijection between the points and the lines of that preserves the incidence relation.
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An orbital plane as viewed relative to a plane of reference. An orbital plane can also be seen in relative to conic sections, in which the orbital path is defined as the intersection between a plane and a cone. Parabolic (1) and hyperbolic (3) orbits are escape orbits, whereas elliptical and circular orbits (2) are captive. The orbital plane of a revolving body is the geometric plane in which its orbit lies.
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A rainbow is perceived as a circle in the sky; and its contributing light rays form a cone. In contrast, a dewbow is perceived as the intersection of that cone and the ground. If the ground is flat and horizontal, and the sun is low in the sky, the dew bow is a hyperbola. Theoretically, when the sun is high, the intersection might be another conic section, like a parabola or an ellipse.
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The equation of a conic section in the variable trilinear point x : y : z is :rx^2+sy^2+tz^2+2uyz+2vzx+2wxy=0. It has no linear terms and no constant term. The equation of a circle of radius r having center at actual-distance coordinates (a', b', c' ) is :(x-a')^2\sin 2A+(y-b')^2\sin 2B+(z-c')^2\sin 2C=2r^2\sin A\sin B\sin C.
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Pluteus nevadensis is a species of fungus in the agaric family Pluteaceae. Described as new to science in 2010, the species is known only from subtropical and pine forests in Mexico, where it grows on rotting pine and oak wood. Fruit bodies (mushrooms) have red-orange caps up to in diameter with a shape ranging from conic, convex, or flattened, depending on their age. The silky yellow stems are up to long.
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In a finite projective plane (not necessarily Desarguesian) a set of points such that no three points of are collinear (on a line) is called a . If the plane has order then , however the maximum value of can only be achieved if is even. In a plane of order , a -arc is called an oval and, if is even, a -arc is called a hyperoval. Every conic in the Desarguesian projective plane PG(2,), i.e.
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Proof: can be done (like the properties above) for the unit parabola y = x^2. Application: This property can be used to determine the direction of the axis of a parabola, if two points and their tangents are given. An alternative way is to determine the midpoints of two parallel chords, see section on parallel chords. Remark: This property is an affine version of the theorem of two perspective triangles of a non-degenerate conic.
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The milk-white shell has an elongate-conic shape. Its length measures 5.2 mm. The 2½ whorls of the protoconch form a depressed, helicoid spire, the axis of which is at right angles to that of the succeeding turns, in the first of which it is about one-fifth immersed. The nine whorls of the teleoconch are slightly rounded on the anterior two-thirds between the sutures, the posterior third forming a strong sloping shoulder.
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The changes in the use of military maps was also part of the modern Military revolution, which changed the need for information as the scale of conflict increases as well. This created a need for maps to help with "... consistency, regularity and uniformity in military conflict." The final form of the equidistant conic projection was constructed by the French astronomer Joseph-Nicolas Delisle in 1745. The Swiss mathematician Johann Lambert invented several hemispheric map projections.
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Khayyám obtained the solutions of these equations by finding the intersection points of two conic sections. This method had been used by the Greeks, but they did not generalize the method to cover all equations with positive roots. Sharaf al-Dīn al-Ṭūsī (? in Tus, Iran – 1213/4) developed a novel approach to the investigation of cubic equations—an approach which entailed finding the point at which a cubic polynomial obtains its maximum value.
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Poles and polars were defined by Joseph Diaz Gergonne and play an important role in his solution of the problem of Apollonius. In planar dynamics a pole is a center of rotation, the polar is the force line of action and the conic is the mass–inertia matrix.John Alexiou Thesis, Chapter 5, pp. 80–108 The pole–polar relationship is used to define the center of percussion of a planar rigid body.
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Winding the trompo Basic throw Playing with a trompo consists of throwing the top and having it spin on the floor. Due to its shape, a trompo spins on its axis and swirls around its conic tip which is usually made of iron or steel. A trompo uses a string wrapped around it to get the necessary spin needed. The player must roll the cord around the trompo from the metallic tip up.
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The cones are erect, ovoid-conic and 2–3.5 cm long, with 30–50 reflexed seed scales; they are green when immature, turning brown and opening to release the seeds when mature, 4–6 months after pollination. The old cones commonly remain on the tree for many years, turning dull grey- black. It grows at altitudes up to 2,900 m on well-drained soils, avoiding waterlogged ground. The scientific name honours Engelbert Kaempfer.
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Hierholzer studied mathematics in Karlsruhe, and he got his Ph.D. from Ruprecht-Karls-Universität Heidelberg in 1865. His Ph.D. advisor was Ludwig Otto Hesse (1811–1874). In 1870 Hierholzer wrote his habilitation about conic sections (title: Ueber Kegelschnitte im Raum) in Karlsruhe, where he later became a Privatdozent. Hierholzer proved that a connected graph has an Eulerian trail if and only if exactly zero or two of its vertices have an odd degree.
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The dextral or sinistral shell is imperforate and pyramidal-conic; solid and glossy with an obtuse apex. The shell has 6.5 whorls. Shell color varies, but is typically green and light greenish-yellow in oblique streaks on the last two whorls, with a faint green peripheral band and a dark chestnut band bordering the suture below. The preceding whorl is yellow with a chestnut band and the three embryonic whorls are pinkish gray.
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The mature female cones are erect, ovoid-conic, 2–5 cm long, with 30-70 erect or slightly incurved (not reflexed) and downy seed scales; they are green variably flushed red when immature, turning brown and opening to release the winged seeds when mature, 4–6 months after pollination. The old cones commonly remain on the tree for many years, turning dull grey-black. The minimum seed-bearing age is 10–15 years.
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Meanwhile, back in 1848 Salmon had published an undergraduate textbook entitled A Treatise on Conic Sections. This text remained in print for over fifty years, going through five updated editions in English, and was translated into German, French and Italian. Salmon himself did not participate in the expansions and updates of the more later editions. The German version, which was a "free adaptation" by Wilhelm Fiedler, was popular as an undergraduate text in Germany.
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The sides below the lateral line are white, and the only melanophores are scattered along the base of the anal fin. The head of the fish is flat with a rounded conic snout that overhangs a small, central mouth. The eyes are relatively large, and the scales are relatively large and uniform all over the body of the fish. The lateral line is straight and completely pored with about 39-42 scales.
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He proceeded to present geometric solutions to all types of cubic equations using the properties of conic sections.Deborah A. Kent, & David J. Muraki (2016). “A Geometric Solution of a Cubic by Omar Khayyam … in Which Colored Diagrams Are Used Instead of Letters for the Greater Ease of Learners”. The American Mathematical Monthly, 123(2), 149–160. The prerequisite lemmas for Khayyam's geometrical proof include Euclid VI, Prop 13, and Apollonius II, Prop 12.
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He argued that a mirror shaped like the part of a conic section, would correct the spherical aberration that flawed the accuracy of refracting telescopes. His design, the "Gregorian telescope", however, remained un-built. In 1666, Isaac Newton argued that the faults of the refracting telescope were fundamental because the lens refracted light of different colors differently. He concluded that light could not be refracted through a lens without causing chromatic aberrations.
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Arthur Cayley and Felix Klein found an application of the cross-ratio to non- Euclidean geometry. Given a nonsingular conic C in the real projective plane, its stabilizer GC in the projective group acts transitively on the points in the interior of C. However, there is an invariant for the action of GC on pairs of points. In fact, every such invariant is expressible as a function of the appropriate cross ratio.
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The very slender, ovate-conic shell measures 2.6 mm. It is white with a narrow, faint yellow band a little posterior to the middle between the sutures. The whorls of the protoconch are very deeply obliquely immersed in the first of the succeeding turns, above which only the tilted edge of the last volution projects. The five whorls of the teleoconch are flattened, slightly contracted at the sutures, and feebly shouldered at the summits.
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The milk-white shell is elongate-conic. Its length measures 2.9 mm. The whorls of the protoconch are quite large, at least two about three-fourths obliquely immersed. The five whorls of the teleoconch are rather broad between the sutures, well rounded, faintly shouldered at the summit, ornamented with depressed, rounded, rather broad axial ribs, about 19 of which occur upon the second, 20 on the third, and 18 upon the penultimate whorl.
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The white shell is large and has an elongate-conic shape. Its length measures 8.3 mm. The whorls of the protoconch are small, vitreous, planorboid, deeply obliquely immersed in the first of the succeeding turns, above which only the tilted edge of the last volution is visible. The six whorls of the teleoconch are increasing regularly in size, well rounded, very narrowly roundly shouldered at the summits, which renders the sutures well marked.
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Its mature height is unknown because none of the living trees are yet mature, but they could possibly grow to or greater. Its habitat is open secondary woodland, scrub, and grassland mixed with Yunnan pine. The Qiaojia pine has a conic crown with flaky pale gray-green bark becoming dark brown with age, similar to the closely related lacebark pine. The shoots are reddish to greenish brown and may be pubescent or glabrous.
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The ring of covariants is given as follows. The identity covariant U of a ternary cubic has degree 1 and order 3. The Hessian H is a covariant of ternary cubics of degree 3 and order 3. There is a covariant G of ternary cubics of degree 8 and order 6 that vanishes on points x lying on the Salmon conic of the polar of x with respect to the curve and its Hessian curve.
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The hermaphrodite or unisexual flowers are more or less radially symmetric, with a perianth of three or four fleshy tepals connate nearly to the apex, one or two stamens, and an ovary with two or three stigmas. The perianth is persistent in fruit. The fruit wall (pericarp) is membranous. The vertical seed is ellipsoid, with light brown, membranous, hairy seed coat, the hairs can be strongly curved, hooked, or conic, straight or slightly curved.
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Archimedes gives two proofs of the main theorem. The first uses abstract mechanics, with Archimedes arguing that the weight of the segment will balance the weight of the triangle when placed on an appropriate lever. The second, more famous proof uses pure geometry, specifically the method of exhaustion. Of the twenty-four propositions, the first three are quoted without proof from Euclid's Elements of Conics (a lost work by Euclid on conic sections).
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The neutron star (center) emits a beam of radiation from its magnetic poles. The beams are swept along a conic surface around the axis of rotation. A neutron star is a highly dense remnant of a star that is primarily composed of neutrons—a particle that is found in most atomic nuclei and has no net electrical charge. The mass of a neutron star is in the range of 1.2 to 2.1 times the mass of the Sun.
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Leaves in summer Mature Shumard oaks typically reach heights of , trunk diameter is typically , and crown width typically reaches in width. Typical size varies according to region, with larger specimens occurring in the southern portions of its native range in the United States. Record Shumard oaks have been measured at up to tall, with crowns up to in width. Young specimens generally exhibit conic or ovate crowns, with the upper crown filling in as the tree reaches maturity.
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The topography of a diameter (Greek diametros) requires a regular curved figure. Irregularly- shaped areas, addressed in modern times, are not in the ancient game plan. Apollonius has in mind, of course, the conic sections, which he describes in often convolute language: “a curve in the same plane” is a circle, ellipse or parabola, while “two curves in the same plane” is a hyperbola. A chord is a straight line whose two end points are on the figure; i.e.
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The length of the shell attains 27 mm, its diameter 7.4 mm. (Original description) The elongate-conic shell is covered with a very pale, ashy, dehiscent periostracum, which in the type is absent on the base and columella and gives the shell a decidedly bicolored effect, the shell itself appearing white. The protoconch contains 2.5 well rounded, smooth whorls, the last half crossed by a small number of axial riblets. The first postnuclear whorl has two nodulose spiral cords.
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The distantly-spaced, pallid gills have an ascending-adnate attachment to the stem, and one or two tiers of interspersed lamellulae. The cap of M. leptocephala is in diameter, and initially a fat conical shape with the margin pressed close to the stem. As the cap expands, it becomes broadly conic to convex, sometimes broadly bell-shaped, and sometimes convex with a flaring margin. The cap surface has a whitish sheen because of its pruinose coating.
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The whitish gills are narrowly adnate. The cap of M. vitilis is initially conic or bell-shaped, but flattens out in maturity, and typically reaches dimensions of up to . When young, the cap margin is pressed against the stem, but as the cap expands it becomes bell-shaped or somewhat umbonate, and the margin flattens out or curves inward. The cap surface is initially hoary but soon becomes polished and slimy when moist, or shiny when dry.
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The cap of M. sanguinolenta is either convex or conic when young, with its margin pressed against the stipe. As it expands, it becomes broadly convex or bell-shaped, ultimately reaching a diameter of . The surface is initially covered with a dense whitish-grayish coating or powder that is produced by delicate microscopic cells, but these cells soon collapse and disappear, leaving the surface naked and smooth. The surface is moist with an opaque margin that soon developing furrows.
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Pholiotina cyanopus is a small saprotrophic mushroom with a conic to broadly convex cap which is smooth and colored ocher to cinnamon brown. It is usually less than 25 mm across and the margin is striate, often with fibrous remnants of the partial veil. The gills are adnate and close, colored cinnamon brown with whitish edges near the margin, darkening in age. The spores are cinnamon brown, smooth and ellipsoid with a germ pore, measuring 8 × 5 micrometers.
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From the river, the house appears as a monumental elevation flanked by two corner towers. The facade and hip slopes of the roof present an overhang of unusual proportions, in a muted reference to the Regency style. The conic roof atop the stair tower built following a fire in 1892 is representative of the Queen Anne Revival. Finally, interior door openings between adjoining rooms were aligned to create particular interior perspectives, in keeping with French architectural tradition.
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In algebraic geometry, a conic bundle is an algebraic variety that appears as a solution of a Cartesian equation of the form : X^2 + aXY + b Y^2 = P (T).\, Theoretically, it can be considered as a Severi–Brauer surface, or more precisely as a Châtelet surface. This can be a double covering of a ruled surface. Through an isomorphism, it can be associated with a symbol (a, P) in the second Galois cohomology of the field k.
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Between species of Ulota, there is variation in the length of the seta which can be a useful trait in classifying species. The sporangia have peristome teeth are diplolepidous, with 8 to 16 exostome teeth and 8 endostome teeth. The sporangia sit on top of a seta which attaches to the gametophyte at the apex of the shoot. The calyptra covers the developing sporangium and is typically conic, split at the base, and can be naked or hairy.
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Pinus roxburghii is a large tree reaching with a trunk diameter of up to , exceptionally . The bark is red-brown, thick and deeply fissured at the base of the trunk, thinner and flaky in the upper crown. The leaves are needle-like, in fascicles of three, very slender, long, and distinctly yellowish green. The cones are ovoid conic, long and broad at the base when closed, green at first, ripening glossy chestnut-brown when 24 months old.
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Their clypeus have 4 macrosetae, which are equidistant across the middle. The surface of the first segment is almost smooth and have dorsum of segments that are coriaceus and shining at the end of the body. The metazonites ventral surface is conic and tuberculate at the same time, and is located next to the keels, or rather to the posterior base which is next to it. Tubercles are continued throughout the surface and are advancing into the posterior margin.
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Pencils of confocal ellipses and hyperbolas In geometry, two conic sections are called confocal, if they have the same foci. Because ellipses and hyperbolas possess two foci, there are confocal ellipses, confocal hyperbolas and confocal mixtures of ellipses and hyperbolas. In the mixture of confocal ellipses and hyperbolas, any ellipse intersects any hyperbola orthogonally (at right angles). Parabolas possess only one focus, so, by convention, confocal parabolas have the same focus and the same axis of symmetry.
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The fruit body of Agaricus deserticola can grow up to in height. Fresh specimens are usually white, but will age to a pale tan; dried fruit bodies are light gray or tan mixed with some yellow. The cap is in diameter, initially conic, later becoming convex to broadly convex as it matures. The cap is composed of three distinct tissue layers: an outer volval layer, a middle cuticular layer (cutis), and an inner (tramal) layer which supports the gleba.
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The elongate-conic shell tapers to an extremely slender apex. The polished shell is white, with a slight suffusion of brown at the apex and near the aperture. Its length measures 17.3 mm. The two whorls of the protoconch are large, compared with the early whorls of the teleoconch, helicoid, depressed, smooth, having their axis almost at a right angle to the axis of the later whorls and extending beyond the outline of these on the left side.
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The base of the stem is pallid and covered with coarse white hairs. The cap of M. galopus is egg- shaped when young, later becoming conic to somewhat bell-shaped, and eventually reaching a diameter of . In age it often has a margin curved inward, and a prominent umbo. The cap surface has a hoary sheen (remnants of the universal veil that once covered the immature fruit body) that soon sloughs off, leaving it naked and smooth.
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The church is structured by six asymmetric prefabricated concrete frames, or arches in descending size towards the chancel. They support a series of prefabricated light scoops, which are conic sections, giving the church its distinctive exterior profile, which some liken to an abstraction of the local Apennine mountains. The facades are faced with mortared stone, and the roof is copper sheeting. The interior is mostly whitewashed plaster, which advantageously reflects northern light brought in from the scoops above.
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The broadly conic shell is milk- white. Its length measures 4 mm. The whorls of the protoconch are large, obliquely immersed in the first of the succeeding turns, above which the tilted edge of the last volution only projects, which shows five strong spiral threads. The five whorls of the teleoconch are well rounded, strongly contracted at the sutures, appressed at the summits with a sloping shoulder that extends from the summit to the second spiral keel.
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Rasterising a circle by the Bresenham algorithm In computer graphics, the midpoint circle algorithm is an algorithm used to determine the points needed for rasterizing a circle. Bresenham's circle algorithm is derived from the midpoint circle algorithm. The algorithm can be generalized to conic sections. The algorithm is related to work by PittewayPitteway, M.L.V., "Algorithm for Drawing Ellipses or Hyperbolae with a Digital Plotter", Computer J., 10(3) November 1967, pp 282-289 and Van Aken.
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In 1970 Danny Cohen presented at the "Computer Graphics 1970" conference in England a linear algorithm for drawing ellipses and circles. In 1971, L. B. Smith published similar algorithms for all conic sections and proved them to have good properties. These algorithms need only a few multiplications and additions to calculate each vector. It is beneficial to use a parametric formulation in computer graphics because the density of points is greatest where there is the most curvature.
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Species in the genus Amphidromus usually have smooth, glossy, brightly colored, elongate or conic, dextrally or sinistrally coiled shells. The shells are moderately large, ranging from to in maximum dimension, having from 6 to 8 convex whorls. Their color pattern is usually monochromatic yellowish or greenish, but can be variegated. The aperture is oblique or ovate in shape, without any teeth or folds, and with the aperture height ranging from two-fifths to one-third of total shell height.
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The height of the shell attains 6½ mm. The dull white, imperforate shell has an ovate-conic, subventricose shape. The apex is rather obtuse. The shell is ornamented with strong spiral subnodose ribs, decussated by elevated rib-striae cutting the interstices into square pits, of which there are 3 or 4 series on the third whorl, 4 on the penultimate, and 7 on the last ; The five, rounded whorls are separated by a deep, subcanaliculate suture.
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When only two gravitational bodies interact, their orbits follow a conic section. The orbit can be open (implying the object never returns) or closed (returning). Which it is depends on the total energy (kinetic + potential energy) of the system. In the case of an open orbit, the speed at any position of the orbit is at least the escape velocity for that position, in the case of a closed orbit, the speed is always less than the escape velocity.
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Outside a specific state plane zone accuracy rapidly declines, thus the system is not useful for regional or national mapping. Most state plane zones are based on either a transverse Mercator projection or a Lambert conformal conic projection. The choice between the two map projections is based on the shape of the state and its zones. States that are long in the east–west direction are typically divided into zones that are also long east–west.
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"Cubic equation and intersection of conic sections" the first page of two-chaptered manuscript kept in Tehran University. Tusi's commentaries on Khayyam's treatment of parallels made its way to Europe. John Wallis, professor of geometry at Oxford, translated Tusi's commentary into Latin. Jesuit geometer Girolamo Saccheri, whose work (euclides ab omni naevo vindicatus, 1733) is generally considered as the first step in the eventual development of non-Euclidean geometry, was familiar with the work of Wallis.
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Halystina umberlee is a very small species, barely reaching a shell height of 2 mm. It has a rounded, conic to turbinate shell, with relatively thick walls and up to 5 whorls. Its bulbous protoconch consists of a single whorl with a pitted surface, and the protoconch-teleoconch transition is marked by a thin line. The teleoconch has 4 convex whorls, sculptured by delicate spiral cordlets crossed by axial threads, forming a delicate net-like pattern.
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The species has a shell height of 1.8 mm and a shell width of 1.2 mm. The shell is greatly variable, taller and slenderer than those of its relatives. It is smooth, transparent and has a conic shape with approximately 5 slightly shouldered whorls, sometimes with an obtuse keel. The opening (aperture) is taller than wide, visible in the shells of the northernmost cave (Pivnica špilja), but hardly pronounced in shells from its other known locality, Jama na Škrilama.
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Here the "ninth intersection" cannot lie on the conic by genericity, and hence it lies on . The Cayley–Bacharach theorem is also used to prove that the group operation on cubic elliptic curves is associative. The same group operation can be applied on a cone if we choose a point on the cone and a line in the plane. The sum of and is obtained by first finding the intersection point of line with , which is .
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The small, slender shell is elongate-conic. It measures 2.4 mm. The two and one-half whorls of the protoconch form a moderately elevated helicoid spire, whose axis is at right angles to that of the succeeding turns, in the first of which it is about one-fifth immersed. The six whorls of the teleoconch overhang and are strongly contracted at the sutures, appressed at the summit, angulated at the posterior extremity of the anterior third.
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While a student at MIT, Steven Anson Coons was employed by the Chance Vought Aircraft Company, in the Master Dimensions Department. He developed a new conic curve based on the unit square. He published a report entitled An Analytic Method for Calculations of the Contours of Double Curved Surfaces. The surface was controlled by one through seventh order polynomials and each curve was express as being one unit long and the element plane in a unit square.
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The nickel particles located in filamentous carbon that is grown in methane and hydrogen gas between and tend to be pear-shaped at the higher end of the temperature range. At higher temperatures, the metal particle becomes deformed. The length of the conic structure of the filaments also increases with temperature. When a copper and silica catalyst is exposed to methane and hydrogen at , hollow, long filamentous carbon structures were formed, and these also contained drops of metal.
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Qvist's theorem on finite ovals In projective geometry Qvist's theorem, named after the Finnish mathematician Bertil Qvist, is a statement on ovals in finite projective planes. Standard examples of ovals are non-degenerate (projective) conic sections. The theorem gives an answer to the question How many tangents to an oval can pass through a point in a finite projective plane? The answer depends essentially upon the order (number of points on a line −1) of the plane.
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Henri Laurens, 1920, Le Petit boxeur, 43 cm, reproduced in Život 2 (1922) Some time after Joseph Csaky's 1911-14 sculptural figures consisting of conic, cylindrical and spherical shapes, a translation of two-dimensional form into three-dimensional form had been undertaken by the French sculptor Henri Laurens. He had met Braque in 1911 and exhibited at the Salon de la Section d'Or in 1912, but his mature activity as a sculptor began in 1915 after experimenting with different materials.
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All prime polysphericons have two edges made of one or more circular arcs and four vertices. All of them, but the sphericon, have surfaces that consist of one kind of conic surface and one, or more, conical or cylindrical frustum surfaces. Two-disc rollers are made of two congruent symmetrical circular or elliptical sectors. The sectors are joined to each other such that the planes in which they lie are perpendicular to each other, and their axes of symmetry coincide.
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Psilocybe weilii caps range from (2)3 to 6(8.5) cm in diameter and are obtusely conic to convex to campanulate. The margin is incurved or inrolled when young, becoming irregularly lobulated then straight with age. Psilocybe weilii are subumbonate, hygrophanous, glabrous, and subviscid when moist from the separable gelatinous pellicle. It is translucent-striate at the margin, and purple brown or chestnut brown to dark brown, fading to buff or straw yellow as it dries, with the center remaining blackish brown.
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The first incisor in the upper jaw is low and broad, the broadest of all teeth in front of the true molars. The second is nearly as broad and comparable in shape. The third incisor and the canine are simple and rounded and about ¼ of the other incisors. The teeth in the lower jaw compare to those in the upper jaw, but the second incisor has an additional conic cusp at its back, there is no third incisor and the canine is minute.
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Mycena sanguinolenta, commonly known as the bleeding bonnet, the smaller bleeding Mycena, or the terrestrial bleeding Mycena, is a species of mushroom in the family Mycenaceae. It is a common and widely distributed species, and has been found in North America, Europe, Australia, and Asia. The fungus produces reddish-brown to reddish-purple fruit bodies with conic to bell- shaped caps up to wide held by slender stipes up to high. When fresh, the fruit bodies will "bleed" a dark reddish-purple sap.
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The length of the shell attains 8.7 mm, its diameter 3.1 mm. (Original description) The small, elongate-conic shell is yellowish white. The first one-half of the protoconch whorl is well rounded, smooth, the last half is marked by a few rather distantly spaced, slightly protractively slanting axial riblets. The postnuclear are whorls well rounded, the first marked by three slender spiral cords, of which the anterior two increase more rapidly in size than the first one, which remains rather feeble.
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Abies pinsapo is an evergreen conifer growing to 20–30 m tall, with a conic crown, sometimes becoming irregular with age. The leaves are 1.5–2 cm long, arranged radially all round the shoots, and are strongly glaucous pale blue-green, with broad bands of whitish wax on both sides. The cones are cylindrical, 9–18 cm long, greenish-pink to purple before maturity, and smooth with the bract scales short and not exserted. When mature, they disintegrate to release the winged seeds.
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The leaves are needle-like, 12–22 mm long, rhombic in cross-section, dark bluish-green with conspicuous stomatal lines. The cones are cylindric-conic, 4–8 cm long and 2 cm broad, maturing pale brown 5–7 months after pollination, and have stiff, smoothly rounded scales. Its population is stable though low, and there are no known protocols that protect it. It is found mostly in the northern Korean Peninsula near the Yalu River, and in Siberia near the Ussuri River.
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René Descartes and Pierre Fermat both applied their newly discovered analytic geometry to the study of conics. This had the effect of reducing the geometrical problems of conics to problems in algebra. However, it was John Wallis in his 1655 treatise Tractatus de sectionibus conicis who first defined the conic sections as instances of equations of second degree. Written earlier, but published later, Jan de Witt's Elementa Curvarum Linearum starts with Kepler's kinematic construction of the conics and then develops the algebraic equations.
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Thus, in Euclidean geometry three non-collinear points determine a circle (as the circumcircle of the triangle they define), but four points in general do not (they do so only for cyclic quadrilaterals), so the notion of "general position with respect to circles", namely "no four points lie on a circle" makes sense. In projective geometry, by contrast, circles are not distinct from conics, and five points determine a conic, so there is no projective notion of "general position with respect to circles".
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It is a medium-sized evergreen tree growing to 25–40 m tall, and with a trunk diameter of up to 1.5 m. The shoots are orange-brown, with scattered pubescence. The leaves are needle-like, 1–2.5 cm long, rhombic in cross-section, greyish-green to bluish-green with conspicuous stomatal lines. The cones are cylindric-conic, 6–15 cm long and 2–3 cm broad, maturing pale brown 5–7 months after pollination, and have stiff, rounded to bluntly pointed scales.
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Chesskid features no advertising. Chesskid.com has run a yearly online championship called CONIC (the ChessKid Online National Invitational Championship), since 2012 which is recognized by the United States Chess Federation. According to David Petty, the event organizer in 2013, Chesskid has made agreements and partnerships with many chess associations to bring the educational benefit of chess to children in schools. In 2014, for a trial period, all signups to the ICA (Illinois Chess Association) included a free gold member subscription to Chesskid.
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The delicate stipe rests atop a flat circular disc. The cap of M. stylobates is in diameter, and depending on its age may range in shape from obtusely conic to convex to bell-shaped to flattened. The structure of the cap margin also depends on the age of the mushroom, progressing from straight or curved inward slightly, to margin flaring or curved backward. The cap surface is smooth, although if viewed with a magnifying glass, minute spines can be seen.
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These points of intersection are the defined to be the foci of C. In other words, a point P is a focus if both PI and PJ are tangent to C. When C is a real curve, only the intersections of conjugate pairs are real, so there are m in a real foci and m2−m imaginary foci. When C is a conic, the real foci defined this way are exactly the foci which can be used in the geometric construction of C.
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If a function of the form y=f(x) cannot be postulated, one can still try to fit a plane curve. Other types of curves, such as conic sections (circular, elliptical, parabolic, and hyperbolic arcs) or trigonometric functions (such as sine and cosine), may also be used, in certain cases. For example, trajectories of objects under the influence of gravity follow a parabolic path, when air resistance is ignored. Hence, matching trajectory data points to a parabolic curve would make sense.
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Around this collar an infinite rope sling runs through two blocks to a winch, powered by hand or an electric motor. In this way the sail is rolled onto the mast when less area is needed or when the sailing is finished. As a result of the conic mast, the clew will move up the less sail that exposed. As a result of the mast taper the clew will end up higher and higher the closer it is to the mast.
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The shell height varies between 16 mm and 35 mm. The elevated- conic shell is imperforate and rather thin. This species is distinguished by its brilliantly colored shell, which is lustrous with a gold field, dotted with brown on the spiral rows of grains, the periphery or lower edge of each whorl encircled by a zone of violet or magenta stripes, the axis surrounded by a tract of the same. The brilliance of the colors fades somewhat once the animal dies.
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Psilocybe tampanensis is a very rare psychedelic mushroom in the family Strophariaceae. Originally collected in the wild in a sandy meadow near Tampa, Florida in 1977, the fungus has never again been reported in Florida, but was later collected in Mississippi. The original Florida specimen was cloned, and descendants remain in wide circulation. The fruit bodies (mushrooms) produced by the fungus are yellowish-brown in color with convex to conic caps up to in diameter atop a thin stem up to long.
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Inocybe aeruginascens is a small mycorrhizal mushroom with a conic to convex cap which becomes plane in age and is often fibrillose near the margin. It is usually less than 5 cm across, has a slightly darker blunt umbo and an incurved margin when young. The cap color varies from buff to light yellow brown, usually with greenish stains which disappear when the mushroom dries. The gills are adnate to nearly free, numerous, colored pale brown, grayish brown, or tobacco brown.
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Under certain conditions it was determined that this ground state variety was a conifold (P. Green & T.Hubsch, 1988; T. Hubsch, 1992) with isolated conic singularities over a certain base with a 1-dimensional exocurve (termed exo-strata) attached at each singular point. T. Hubsch and A. Rahman determined the (co)-homology of this ground state variety in all dimensions, found it compatible with Mirror symmetry and String Theory but found an obstruction in the middle dimension (T. Hubsch and A. Rahman, 2005).
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Leaves and mature cones It is a large deciduous coniferous tree reaching tall, with a trunk up to diameter. The largest known western larch is tall and in circumference with a crown, located at Seeley Lake, Montana. The crown is narrow conic; the main branches are level to upswept, with the side branches often drooping. The shoots are dimorphic, with growth divided into long shoots (typically long) and bearing several buds, and short shoots only long with only a single bud.
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It is widely grown as an ornamental tree throughout Europe. The cultivar 'Brabant' has a strong central stem and a symmetrical conic crown. The cultivar 'Petiolaris' (pendent or weeping silver lime) differs in longer leaf petioles 4–8 cm long and drooping leaves; it is of unknown origin and usually sterile, and may be a hybrid with another Tilia species. It is very tolerant of urban pollution, soil compaction, heat, and drought, and would be a good street tree in urban areas.
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The cap is obtusely conic to convex, and does not expand to become flattened with age; it reaches in diameter. Its margin is bent in slightly at first but soon straightens. The cap surface is smooth except for a faint fringe at the margin from a rudimentary veil, sticky, hygrophanous but opaque when moist, deep brown in the center and somewhat darker brown near the margin. As the mushroom matures, it fades slowly in the center to a dull cinnamon color.
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Young fruit bodies of C. vanduzerensis are covered with a slimy universal veil; the slime layer persists on the cap of young mushrooms, or in moist weather. The shape of the cap is oval to conical with the margin initially appressed, expanding to broadly conic or somewhat flattened in maturity, eventually reaching diameters of . The cap color is initially chestnut-brown to black, but becomes paler brown as it matures. The surface is radially wrinkled or corrugated, especially near the margin.
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During his time in Kushtia, Hossain, coming from a relatively poor family, supported himself by various scholarships, lodged at nearby homes as house tutors and later settled at a hostel. Among the teachers, he specially later recalled of Jyotindranath Roy and Jatindra Mohan Biswas. During his years at the school, Jyotindranath Roy, an accomplished teacher of Mathematics and Sciences, laid Hossain's foundation in algebra, geometry, conic section and mechanics. Mr. Roy, recognizing Hossain's interest in mathematics, introduced the mechanics course solely for him.
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Originally, before brake drums were available, frying pans were used (Pérez I 1988:310, Pérez II 1988:23, etc.) and possibly plow blades as well (Pérez I 1988:106 and 134). The second category is the bocuses (sing. bocú alt. pl. bocúes), also called fondos ("bottoms"). > “The bokú is a single-headed drum, skin nailed to the shell, shell open at > one end, long, shaped like a conic section and made of staves with iron > hoops that circle them and hold them together.
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This theorem is a generalization of Pappus's (hexagon) theorem – Pappus's theorem is the special case of a degenerate conic of two lines. Pascal's theorem is the polar reciprocal and projective dual of Brianchon's theorem. It was formulated by Blaise Pascal in a note written in 1639 when he was 16 years old and published the following year as a broadside titled "Essay pour les coniques. Par B. P.", translation Pascal's theorem is a special case of the Cayley–Bacharach theorem.
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Degenerate conics follow by continuity (the theorem is true for non-degenerate conics, and thus holds in the limit of degenerate conic). A short elementary proof of Pascal's theorem in the case of a circle was found by , based on the proof in . This proof proves the theorem for circle and then generalizes it to conics. A short elementary computational proof in the case of the real projective plane was found by We can infer the proof from existence of isogonal conjugate too.
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A classification of polarities over arbitrary fields follows from the classification of sesquilinear forms given by Birkhoff and von Neumann. Orthogonal polarities, corresponding to symmetric bilinear forms, are also called ordinary polarities and the locus of absolute points forms a non-degenerate conic (set of points whose coordinates satisfy an irreducible homogeneous quadratic equation) if the field does not have characteristic two. In characteristic two the orthogonal polarities are called pseudopolarities and in a plane the absolute points form a line.
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Further Mathematics is available as a second and higher mathematics course at A Level (now H2), in addition to the Mathematics course at A Level. Students can pursue this subject if they have A2 and better in 'O' Level Mathematics and Additional Mathematics, depending on the school. Some topics covered in this course include mathematical induction, complex number, polar curve and conic sections, differential equations, recurrent equations, matrices and linear spaces, numerical methods, random variables and hypothesis testing and confidence intervals.
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A circular conical surface In geometry, a (general) conical surface is the unbounded surface formed by the union of all the straight lines that pass through a fixed point -- the apex or vertex -- and any point of some fixed space curve -- the directrix -- that does not contain the apex. Each of those lines is called a generatrix of the surface. Every conic surface is ruled and developable. In general, a conical surface consists of two congruent unbounded halves joined by the apex.
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The first courses in mathematics were offered in 1760 when undergraduates enrolled in classes such as algebra, trigonometry, geometry, and conic sections. Walter Minto was one of the earliest teachers of mathematics beginning in 1787. By the beginning of the twentieth century, the department became "one of the world's great centers of mathematical teaching and research." President Woodrow Wilson appointed Henry Burchard Fine as dean of the faculty in 1903 and later as the first chairman of the Department of Mathematics in 1905.
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Another approach, used by modern hardware graphics adapters with accelerated geometry, can convert exactly all Bézier and conic curves (or surfaces) into NURBS, that can be rendered incrementally without first splitting the curve recursively to reach the necessary flatness condition. This approach also allows preserving the curve definition under all linear or perspective 2D and 3D transforms and projections. Font engines, like FreeType, draw the font's curves (and lines) on a pixellated surface using a process known as font rasterization.
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Euclid also wrote extensively on other subjects, such as conic sections, optics, spherical geometry, and mechanics, but only half of his writings survive. Archimedes used the method of exhaustion to approximate the value of pi. Archimedes (c. 287–212 BC) of Syracuse, widely considered the greatest mathematician of antiquity, used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, in a manner not too dissimilar from modern calculus.
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To Colin Maclaurin's Account of Sir Isaac Newton's Philosophical Discoveries, 4to, London, 1748, which he saw through the press for the benefit of the author's children, he prefixed an account of his life. Another edition was issued in 1750, 8vo. He also edited the illustrations of perspective from conic sections, entitled Neutoni Genesis Curvarum per Umbras, &c.;, 8vo, London, 1746. He contemplated a complete edition of Newton's works, and by 1766 had found a publisher in Andrew Millar, but increasing infirmities obliged him to abandon the undertaking.
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The shell grows to a length of 6.8 mm, its diameter 2.5 mm. (Original description) The small, vitreous, semitranslucent shell has an elongate-conic shape.. The protoconch contains 1.5,well rounded, smooth whorls. The postnuclear whorls are moderately well rounded, marked by rather strong, almost vertical axial ribs, which become weak toward the summit and which attain their largest development on the posterior third of the whorls. On the first whorl on the teleoconch these ribs are cusped; on the later ones they become less elevated.
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Steerable Rogallo kites usually have a pair of bridles setting a fixed pitch, and use two strings, one on each side of the kite, to change the roll. Rogallo also developed a series of soft foil designs in the 1960s which have been modified for traction kiting. These are double keel designs with conic wings and a multiple attachment bridle which can be used with either dual line or quad line controls. They have excellent pull, but suffer from a smaller window than more modern traction designs.
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Shell rather small, elongated fusiform, solid, with a moderately long canal. Sculpture consisting of subequal narrow spiral cords, about 10 on the penultimate whorl, the interspaces shallow, much broader than the cords upon the base, where they have a fine spiral thread; axial sculpture formed by numerous vertical broadly rounded ribs, 15 to 20 on the body whorl, where they become obsolete below the periphery. Colour light - yellowish, the spirals reddish - brown. Spire elevated conic, of the same height as the aperture with canal; outlines straight.
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For a given conic C, a point Z has a corresponding straight the polar of Z and Z is the pole of this straight: Through Z draw two secants through C crossing at AD and BC. Consider the tetrastim ABCD which has Z as a codot. Then the polar of Z is the straight through the other two codots of ABCD (page 25). Continuing with conics, conjugate diameters are straights, each of which is the polar of the figurative point of the other (page 32).
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On Conoids and Spheroids () is a surviving work by the Greek mathematician and engineer Archimedes ( 287 BC – 212 BC). Comprising 32 propositions, the work explores properties of and theorems related to the solids generated by revolution of conic sections about their axes, including paraboloids, hyperboloids, and spheroids. The principal result of the work is comparing the volume of any segment cut off by a plane with the volume of a cone with equal base and axis. The work is addressed to Dositheus of Pelusium.
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Its lip is attached to the apex of its thin, un- hornlike column foot (2-2.4 mm long by 1 mm wide) is ovate-triangular and purple-tinged, with a rounded to obtuse apex, and a base decurrent into a long, entire, glabrous, membranaceous, three-nerved claw. The column (0.8–1 mm long), has stubby stylids at its apex, and its foot is 2 mm long. Its triangularly conic anther is white with an area of red, and its two pollinia are ovoid to ellipsoid.
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Balsam fir is a small to medium-size evergreen tree typically tall, occasionally reaching a height of . The narrow conic crown consists of dense, dark-green leaves. The bark on young trees is smooth, grey, and with resin blisters (which tend to spray when ruptured), becoming rough and fissured or scaly on old trees. The leaves are flat and needle-like, long, dark green above often with a small patch of stomata near the tip, and two white stomatal bands below, and a slightly notched tip.
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His Dissenters' Plea, Birmingham (1790), was reckoned by Charles James Fox the best publication on the subject. He was an early advocate of the abolition of the slave trade. In 1794 he published his treatise on conic sections, while he was agitating against measures for the suppression of public opinion, which culminated in the Seditious Meetings Act 1795. Towards the close of 1797, after a fruitless application to Thomas Belsham, Walker was invited to succeed Thomas Barnes as professor of theology in Manchester College.
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Female cones of Agathis macrophyllaIt is a large evergreen tree, reaching 40 m in height and 3 m in diameter. It possesses the mottled, shedding bark that is characteristic of other kauri species. Young trees are narrow and conic in shape, but begin to grow a wider, deeper canopy after attaining a trunk diameter of 30–50 cm. In mature specimens, the trunk is generally straight or slightly tapered and clear for 15–20 m before branching into a spreading canopy up to 35 m in diameter.
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The fruit bodies of Psilocybe subcaerulipes have caps that are in diameter, initially conic or bell-shaped but expanding to become convex, then finally somewhat flattened in maturity. A well-defined umbo (a rounded elevation resembling a nipple) is typically present. The cap color is chestnut brown when wet, but the species is hygrophanous, and when dried, changes color to become a lighter shade of brown. As is characteristic of psilocybin- containing species, P. subcaerulipes stains blue where it has been bruised or injured.
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XCOM Multimedia Communications and CXSAT were makers of digital satellite receiver decoder. In 2005, the company sold the former headquarter Conic Investment Building which was located in Hung Hom to Global Coin Limited, a subsidiary Cheung Kong Holdings, for HK$330 million. The company also owned 14.29% shares of APT Satellite International (via a subsidiary CASIL Satellite), the parent company of listed company APT Satellite Holdings, the operator Apstar satellites. CASIL Satellite was sold to CASIL's parent company CASC in 2011 for HK$132.3 million.
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Suter, Die Mathematiker und Astronomen der Araber (75-76, 1900). (PDF version) Engraving of al-Qūhī's perfect compass to draw conic sections Al-Qūhī was the leader of the astronomers working in 988 AD at the observatory built by the Buwayhid amir Sharaf al-Dawla in Badhdad. He wrote a treatise on the astrolabe in which he solves a number of difficult geometric problems. In mathematics he devoted his attention to those Archimedean and Apollonian problems leading to equations higher than the second degree.
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TLI targeting and lunar transfers are a specific application of the n body problem, which may be approximated in various ways. The simplest way to explore lunar transfer trajectories is by the method of patched conics. The spacecraft is assumed to accelerate only under classical 2 body dynamics, being dominated by the Earth until it reaches the Moon's sphere of influence. Motion in a patched-conic system is deterministic and simple to calculate, lending itself for rough mission design and "back of the envelope" studies.
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Quetelet, Adolphe (1819) "Dissertatio mathematica inauguralis de quibusdam locis geometricis nec non de curva focali" (Inaugural mathematical dissertation on some geometric loci and also focal curves), doctoral thesis (University of Ghent ("Gand"), Belgium). (in Latin) The Dandelin spheres can be used to give elegant modern proofs of two classical theorems known to Apollonius of Perga. The first theorem is that a closed conic section (i.e. an ellipse) is the locus of points such that the sum of the distances to two fixed points (the foci) is constant.
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Heath, Thomas. A History of Greek Mathematics, page 119 (focus-directrix property), page 542 (sum of distances to foci property) (Clarendon Press, 1921). Neither Dandelin nor Quetelet used the Dandelin spheres to prove the focus-directrix property. The first to do so may have been Pierce Morton in 1829,Numericana's Biographies: Morton, Pierce or perhaps Hugh Hamilton who remarked (in 1758) that a sphere touches the cone at a circle which defines a plane whose intersection with the plane of the conic section is a directrix.
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The hypothetical motion that the body follows under the gravitational effect of one other body only is typically a conic section, and can be readily modeled with the methods of geometry. This is called a two-body problem, or an unperturbed Keplerian orbit. The differences between the Keplerian orbit and the actual motion of the body are caused by perturbations. These perturbations are caused by forces other than the gravitational effect between the primary and secondary body and must be modeled to create an accurate orbit simulation.
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For an oval to be a conic the oval and/or the plane has to fulfill additional conditions. Here are some results: #An oval in an arbitrary projective plane, which fulfills the incidence condition of Pascal's theorem or the 5-point degeneration of it, is a nondegenerate conic.F. Buekenhout: Plans Projectifs à Ovoides Pascaliens, Arch. d. Math. Vol. XVII, 1966, pp. 89-93. #If is an oval in a pappian projective plane and the group of projectivities which leave invariant is 3-transitive, i.e.
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Illustration of the duality between points and lines, and the double meaning of "incidence". If two lines a and k pass through a single point Q, then the polar q of Q joins the poles A and K of the lines a and k, respectively. The concepts of a pole and its polar line were advanced in projective geometry. For instance, the polar line can be viewed as the set of projective harmonic conjugates of a given point, the pole, with respect to a conic.
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It includes 21 Munros (including Ben Lomond, Ben Lui, Beinn Challuim, Ben More and two peaks called Ben Vorlich) and 20 Corbetts. The park straddles the Highland Boundary Fault which divides it into two distinct regions - lowland and highland - which differ in underlying geology, soil types and topography.Wild Park 2020. p. 55. The change in rock type can most clearly be seen at Loch Lomond itself, as the fault runs across the islands of Inchmurrin, Creinch, Torrinch and Inchcailloch and over the ridge of Conic Hill.
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Unperturbed, two-body, Newtonian orbits are always conic sections, so the Keplerian elements define an ellipse, parabola, or hyperbola. Real orbits have perturbations, so a given set of Keplerian elements accurately describes an orbit only at the epoch. Evolution of the orbital elements takes place due to the gravitational pull of bodies other than the primary, the nonsphericity of the primary, atmospheric drag, relativistic effects, radiation pressure, electromagnetic forces, and so on. Keplerian elements can often be used to produce useful predictions at times near the epoch.
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The magnification in an atom is due to the projection of ions radially away from the small, sharp tip. Subsequently, in the far field, the ions will be greatly magnified. This magnification is sufficient to observe field variations due to individual atoms, thus allowing in field ion and field evaporation modes for the imaging of single atoms. The standard projection model for the atom probe is an emitter geometry that is based upon a revolution of a conic section, such as a sphere, hyperboloid or paraboloid.
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There are many legends about the origin of name Osogovo, but the most famous one is that it was given by the Saxon miners who were mining gold and silver in the region in the past. According to this legend, the name originates from the Old Germanic words "osso" (god) and "gov" (place) which means "a divine place". Osogovo in Bulgaria The mountain itself is a powerful granite massif of crystal rocks. It has a prominent volcanic relief made of conic peaks and volcanic tuff.
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The unit hyperbola has a sector with an area half of the hyperbolic angle Circular vs. hyperbolic angle A unit circle x^2 + y^2 = 1 has a circular sector with an area half of the circular angle in radians. Analogously, a unit hyperbola x^2 - y^2 = 1 has a hyperbolic sector with an area half of the hyperbolic angle. There is also a projective resolution between circular and hyperbolic cases: both curves are conic sections, and hence are treated as projective ranges in projective geometry.
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After returning to Copenhagen, Zeuthen submitted his doctoral dissertation on a new method to determine the characteristics of conic systems in 1865. Enumerative geometry remained his focus up until 1875. In 1871 he was appointed as an extraordinary professor at the University of Copenhagen, as well as becoming an editor of Matematisk Tidsskrift, a position he held for 18 years. For 39 years he served as secretary of the Royal Danish Academy of Sciences and Letters, during which he also lectured at the Polytechnic Institute.
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The IEEE Spectrum has organized a number of competitions on quilt block design, and several books have been published on the subject. Notable quiltmakers include Diana Venters and Elaine Ellison, who have written a book on the subject Mathematical Quilts: No Sewing Required. Examples of mathematical ideas used in the book as the basis of a quilt include the golden rectangle, conic sections, Leonardo da Vinci's Claw, the Koch curve, the Clifford torus, San Gaku, Mascheroni's cardioid, Pythagorean triples, spidrons, and the six trigonometric functions..
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The cap of M. aurantiomarginata ranges in shape from obtusely conic to bell-shaped, and becomes flat in maturity, reaching diameters of . The cap color is variable, ranging from dark olive fuscous (dark brownish- gray) to yellowish-olive in the center, while the margin is orangish. Alexander H. Smith, in his 1947 monograph of North American Mycena species, stated that the caps are not hygrophanous (changing color depending on the level of hydration),Smith (1947), pp. 198–9. while Mycena specialist Arne Aronsen says they are.
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It is a monoecious evergreen tree growing to 25 m tall, with a trunk diameter of up to 1 m. The shoots are orange-brown, with scattered pubescence. The leaves are needle-like, 8–16 mm long, rhombic in cross- section, dark bluish-green with conspicuous stomatal lines. The cones are cylindric-conic, 4–9 cm long and 2 cm broad, maturing pale brown 5–7 months after pollination, and have stiff, smoothly rounded scales 6–18 mm long and 6–12 mm wide.
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On the bell tower, a plaque says that Deustesalvet (Diotisalvi, literally "God Saves You"), architect of the Baptistry, was the designer of the edifice. Inscription It has an octagonal plan and, until the 16th century, it was surrounded by a portico. The central tambour, supported by eight ogival arches, is super-elevated and is surmounted by a conic cusp. The attribution to the Holy Sepulchre is a reference to the latter's relics which were carried in Pisa by archbishop Dagobert after his participation to the First Crusade.
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The presumption that solid and liquid are adjacent states of matter was undercut by Friedrich Reinitzer in 1888 when he noted a cloudy mesophase of cholesteryl benzoate between 145.5 °C and 178.5 °C. The subject was taken up in Germany, and in 1907 also in France by George Friedel and François Grandjean, as they described the "focal conic liquid". Friedel contributed his Mesomorphic States of Matter to the Annales des Physiques in 1922. This two-hundred-page work established much of the current terminology in mesophase physics.
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Another important interpretation of the Brauer group of a field K is that it classifies the projective varieties over K that become isomorphic to projective space over an algebraic closure of K. Such a variety is called a Severi–Brauer variety, and there is a one-to-one correspondence between the isomorphism classes of Severi–Brauer varieties of dimension n−1 over K and the central simple algebras of degree n over K.Gille & Szamuely (2006), section 5.2. For example, the Severi–Brauer varieties of dimension 1 are exactly the smooth conics in the projective plane over K. For a field K of characteristic not 2, every conic over K is isomorphic to one of the form ax2 \+ by2 = z2 for some nonzero elements a and b of K. The corresponding central simple algebra is the quaternion algebraGille & Szamuely (2006), Theorem 1.4.2. :(a,b) = K\langle i,j\rangle/(i^2=a, j^2=b, ij=-ji). The conic is isomorphic to the projective line P1 over K if and only if the corresponding quaternion algebra is isomorphic to the matrix algebra M(2, K).
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The Keroro double platoon was created by the Keroro platoon to stand in for them while they took the day off. The double platoon is easily identifiable from the real one due to their differently shaped eyes, and their somewhat curled feet (and, in Kururu's double case, a conic head), but Fuyuki and Natsumi were unable to notice the difference. However, they were left in invasion mode and tried to invade Earth for real before the real platoon stopped them. The platoon took the robots off again to do their homework, apparently limited by Kururu.
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Florentine world map based on the 1st (modified conic) projection in Jacobus Angelus's 1406 Latin translation of Maximus Planudes's late-13th century rediscovered Greek manuscripts of Ptolemy's 2nd-century Geography. Serica is shown in the far northeast of the world. Serica () was one of the easternmost countries of Asia known to the Ancient Greek and Roman geographers. It is generally taken as referring to North China during its Zhou, Qin, and Han dynasties, as it was reached via the overland Silk Road in contrast to the Sinae, who were reached via the maritime routes.
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He was born at Blandfield House, between Edinburgh and Leith, the son of Alexander Hamilton, Professor of Midwifery at Edinburgh University. He was educated at Edinburgh University and Trinity College, Cambridge, graduating BA in 1816 and MA in 1819. He wrote two textbooks on analytical geometry, The Principles of Analytical Geometry (1826) and An Analytical System of Conic Sections (1828; 5th edn, 1843). He was elected a Fellow of the Royal Society in 1828 as "a gentleman well versed in mathematics", and was also elected FRS (Edinburgh) in 1922, as well as FRAS and FGS.
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The rural village of Tebilhão in the terraced foothills of Arouca The Arouca is a fertile valley, almost entirely enclosed with a mountainous plateau, with only the western edge open to the rest of the country. To the north is the Serra do Gamarão, to the east the conic mountain of Mó and the Serra da Freita ao Sul.,Abel Botelho (1883) and to the south is the ridge of Montemuro (the highest point in the municipality). Here is situated the Pedra Posta, at approximately , relatively close to the Noninha.
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The length of the shell varies between 7.5 mm and 9.2 mm. (Original description) The small, shiny shell has an elongate-conic shape.. Nuclear whorls The protoconch contains 1.5 well rounded, smooth whorls. The postnuclear whorls are moderately well rounded with strongly developed axial ribs, which begin weakly at the summit of the whorls and become strongest at about the anterior termination of the posterior third, again gradually weakening on the base and evanescing on the columella. These ribs on the early whorls are cusped at their highest elevation.
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If the gnomon (the shadow-casting object) is not an edge but a point (e.g., a hole in a plate), the shadow (or spot of light) will trace out a curve during the course of a day. If the shadow is cast on a plane surface, this curve will be a conic section (usually a hyperbola), since the circle of the Sun's motion together with the gnomon point define a cone. At the spring and fall equinoxes, the cone degenerates into a plane and the hyperbola into a line.
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Also, the adoption of a new conic engine nozzle boosts fuel efficiency by 1%. Over its production life, the CRJ family has latterly competed with the Embraer E-Jet family. A re-engining of the CRJ, akin to the rival Embraer E-Jet E2, with newer and more efficient engines, such as the GE Passport, to replace the current GE CF34 powerplants, would be unlikely to overcome the certification expense, primarily as newer engines are larger and heavier, eroding fuel burn improvements that would be achieved on short regional routes.
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The greatest mathematician of antiquity is often held to be Archimedes (c. 287–212 BC) of Syracuse. He developed formulas for calculating the surface area and volume of solids of revolution and used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, in a manner not too dissimilar from modern calculus. Other notable achievements of Greek mathematics are conic sections (Apollonius of Perga, 3rd century BC), trigonometry Hipparchus of Nicaea (2nd century BC), and the beginnings of algebra (Diophantus, 3rd century AD).
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The simplification is achieved by dividing space into various parts by assigning each of the n bodies (e.g. the Sun, planets, moons) its own sphere of influence. When the spacecraft is within the sphere of influence of a smaller body, only the gravitational force between the spacecraft and that smaller body is considered, otherwise the gravitational force between the spacecraft and the larger body is used. This reduces a complicated n-body problem to multiple two-body problems, for which the solutions are the well-known conic sections of the Kepler orbits.
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Older trees in traditional orchards can grow gnarled and hollowed for the tree's entire lifespan. The large (7.6 meter) spherical-shaped canopies of traditional methods differ from various planting systems that use conic, flat planar or v-shaped styles.Traditional apple orchard in Eastwood, Essex Traditional orchards were often intercropped: it was particularly common to use a silvopastoral system that combined fruit trees and pasture. The natural grasses forming the orchard's undergrowth were often grazed by sheep or cows: the English "grass orchard" was particularly associated with cider producing districts.
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Aspide (the Italian name for the adder) is an Italian medium range air-to-air and surface-to-air missile produced by Selenia (now part of the Alenia consortium). It is provided with semi-active radar homing seeker. It is very similar to the American AIM-7 Sparrow, using the same airframe, but at the moment of its introduction, the Aspide was provided with monopulse guide instead of the conic scan, which made it more resistant to ECM and more precise. This innovation appeared on the Sparrows only with the late AIM-7M version.
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One hundred years after him Euclid too shunned neuseis in his very influential textbook, The Elements. The next attack on the neusis came when, from the fourth century BC, Plato's idealism gained ground. Under its influence a hierarchy of three classes of geometrical constructions was developed. Descending from the "abstract and noble" to the "mechanical and earthly", the three classes were: #constructions with straight lines and circles only (compass and straightedge); # constructions that in addition to this use conic sections (ellipses, parabolas, hyperbolas); # constructions that needed yet other means of construction, for example neuseis.
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The circle is a special kind of ellipse, although historically Apollonius considered as a fourth type. Ellipses arise when the intersection of the cone and plane is a closed curve. The circle is obtained when the cutting plane is parallel to the plane of the generating circle of the cone; for a right cone, this means the cutting plane is perpendicular to the axis. If the cutting plane is parallel to exactly one generating line of the cone, then the conic is unbounded and is called a parabola.
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Non-degenerate conic equation: :Ax^2 + Bxy + Cy^2 +Dx + Ey + F = 0, where at least one of the given parameters A, B, and C is non-zero, and x and y are real variables. Pell's equation: :\ x^2 - Py^2 = 1, where P is a given integer that is not a square number, and in which the variables x and y are required to be integers. The equation of Pythagorean triples: :x^2+y^2=z^2, in which the variables x, y, and z are required to be positive integers.
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In 2008 Horst Martini and Margarita Spirova generalized the first of Clifford's circle theorems and other Euclidean geometry using affine geometry associated with the Cayley absolute: :If the absolute contains a line, then one obtains a subfamily of affine Cayley-Klein geometries. If the absolute consists of a line f and a point F on f, then we have the isotropic geometry. An isotropic circle is a conic touching f at F.Martini and Spirova (2008) Use homogeneous coordinates (x,y,z). Line f at infinity is z = 0.
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Different geometries allow different notions of geometric constraints. For example, a circle is a concept that makes sense in Euclidean geometry, but not in affine linear geometry or projective geometry, where circles cannot be distinguished from ellipses, since one may squeeze a circle to an ellipse. Similarly, a parabola is a concept in affine geometry but not in projective geometry, where a parabola is simply a kind of conic. The geometry that is overwhelmingly used in algebraic geometry is projective geometry, with affine geometry finding significant but far less use.
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The Service’s Wetlands Geodatabase contains five units (map areas) that are populated with digital vector data and raster images. These units include the conterminous U.S., Alaska, Hawaii, Puerto Rico and the U.S. Virgin Islands, and the Pacific Trust Territories. Each unit of the geodatabase contains seamless digital map data in ArcSDE geodatabase format. Data are in a single standard projection (Albers Equal-Area Conic Projection), horizontal planar units in meters, horizontal planar datum is the North American Datum of 1983 (also called NAD83), and minimum coordinate precision of one centimeter.
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In his earlier years Wallace was an occasional contributor to Leybourne's Mathematical Repository and the Gentleman's Mathematical Companion. Between 1801 and 1810 he contributed articles on "Algebra", "Conic Sections", "Trigonometry", and several others in mathematical and physical science to the fourth edition of the Encyclopædia Britannica, and some of these were retained in subsequent editions from the fifth to the eighth inclusive. He was also the author of the principal mathematical articles in the Edinburgh Encyclopædia, edited by David Brewster. He also contributed many important papers to the Transactions of the Royal Society of Edinburgh.
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The Kitab al- Istikmal deals with irrational numbers, conic sections, quadrature of the parabolic segment, volumes and areas of various geometric objects, and the drawing of the tangent to a circle, among other mathematical problems. In the work appears an attempt to classify mathematics into Aristotelian categories. The classification includes a chapter for arithmetic, two chapters for geometry and two others for stereometry. Al-Mu'taman is the author of the first known formulation of Ceva's theorem, which was only known in Europe in 1678 in De lineis rectis by the Italian geometer Giovanni Ceva.
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Pinus latteri is a medium-sized to large tree, reaching 25–45 m tall and with a trunk diameter of up to 1.5 m. The bark is orange-red, thick and deeply fissured at the base of the trunk, and thin and flaky in the upper crown. The leaves ('needles') are in pairs, moderately slender, 15–20 cm long and just over 1 mm thick, green to yellowish green. The cones are narrow conic, 6–14 cm long and 4 cm broad at the base when closed, green at first, ripening glossy red-brown.
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Pinus merkusii is a medium-sized to large tree, reaching tall and with a trunk diameter of up to . The bark is orange-red, thick and deeply fissured at the base of the trunk, and thin and flaky in the upper crown. The leaves ("needles") are in pairs, very slender, 15–20 cm long and less than 1 mm thick, green to yellowish green. The cones are narrow conic, 5–8 cm long and 2 cm broad at the base when closed, green at first, ripening glossy red-brown.
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The cones are conic, 10–20 cm long and 4–6 cm broad at the base when closed, green at first, ripening glossy red-brown when 24 months old. They open slowly over the next few years, or after being heated by a forest fire, to release the seeds, opening to 8–12 cm broad. The seeds are 8–10 mm long, with a 20–25 mm wing, and are wind-dispersed. Maritime pine is closely related to Turkish pine, Canary Island pine, and Aleppo pine, which all share many features with it.
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In the case where the conic is a circle, on the extended diameters of the circle, harmonic conjugates with respect to the circle are inverses in a circle. This fact follows from one of Smogorzhevsky's theorems:A.S. Smogorzhevsky (1982) Lobachevskian Geometry, Mir Publishers, Moscow :If circles k and q are mutually orthogonal, then a straight line passing through the center of k and intersecting q, does so at points symmetrical with respect to k. That is, if the line is an extended diameter of k, then the intersections with q are harmonic conjugates.
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Menaechmus' original solution involves the intersection of two conic curves. Other more complicated methods of doubling the cube involve neusis, the cissoid of Diocles, the conchoid of Nicomedes, or the Philo line. Pandrosion, a female mathematician of ancient Greece, found a numerically-accurate approximate solution using planes in three dimensions, but was heavily criticized by Pappus of Alexandria for not providing a proper mathematical proof. Archytas solved the problem in the 4th century BC using geometric construction in three dimensions, determining a certain point as the intersection of three surfaces of revolution.
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Graphic rapresentation of JPL Horizons On-Line Ephemeris System output values JPL Horizons On-Line Ephemeris System provides easy access to key Solar System data and flexible production of highly accurate ephemerides for Solar System objects. Osculating elements at a given epoch are always an approximation to an object's orbit (i.e. an unperturbed conic orbit or a "two-body" orbit). The real orbit (or the best approximation to such) considers perturbations by all planets, a few of the larger asteroids, a few other usually small physical forces, and requires numerical integration.
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The Foucault knife-edge test was described in 1858 by French physicist Léon Foucault as a way to measure conic shapes of optical mirrors.Texereau 1984 pp.68-70 section 2.25 It measures mirror surface dimensions by reflecting light into a knife edge at or near the mirror's centre of curvature. In doing so, it only needs a tester which in its most basic 19th century form consists of a light bulb, a piece of tinfoil with a pinhole in it, and a razor blade to create the knife edge.
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Western hemlock is a large evergreen coniferous tree growing to tall, exceptionally ,Tallest Hemlock, M. D. Vaden, Arborist: Tallest known Hemlock, Tsuga heterophylla and with a trunk diameter of up to . It is the largest species of hemlock, with the next largest (mountain hemlock, T. mertensiana) reaching a maximum of . The bark is brown, thin and furrowed. The crown is a very neat broad conic shape in young trees with a strongly drooping lead shoot, becoming cylindric in older trees; old trees may have no branches in the lowest .
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The cap of M. californiensis is initially conic or bell- shaped, but flattens out in maturity, and typically reaches dimensions of up to . The cap margins (edges) are curved inwards when young, but as they age they become wavy or crenate (with rounded scallops), develop striations (radial grooves) and may even split. The surface of the cap is dull and smooth. Its color ranges from reddish brown to brownish orange in young specimens, with the color fading as the mushroom matures; the center of the cap is usually darker than the margins.
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The length of the varies between 12 mm and 30 mm. The small, imperforate, rather solid shell has a conical shape. The coloration consists of rather broad longitudinal stripes of dark olive-green or red, alternating with stripes of bright pink, bordered with lines of delicate green, and frequently veined with the same tint The stripes are continuous from suture to base, or are displaced or interrupted at the periphery These axial zigzag markings on a dark or pale brown background are characteristic. The spire is low-conic The eroded apex is orange-colored.
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Kig can handle any classical object of the dynamic geometry, but also: # The center of curvature and osculating circle of a curve; # The dilation, generic affinity, inversion, projective application, homography and harmonic homology; # The hyperbola with given asymptotes; # The Bézier curves (2nd and 3rd degree); # The polar line of a point and pole of a line with respect to a conic section; # The asymptotes of a hyperbola; # The cubic curve through 9 points; # The cubic curve with a double point through 6 points; # The cubic curve with a cusp through 4 points.
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Since he was a trained engineer he was offered a job in the British colonial service. This job took him to Egypt where he worked on the construction of the Assiut dam until April 1900. During periods when construction work had to stop due to floods, he studied mathematics from some textbooks he had with him, such as Jordan's Cours d'Analyse and Salmon's text on the analytic geometry of conic sections. He also visited the Cheops pyramid and made measurements which he wrote up and published in 1901.
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Point F is a focus point for the red ellipse, green parabola and blue hyperbola. In geometry, focuses or foci (, ), singular focus, are special points with reference to which any of a variety of curves is constructed. For example, one or two foci can be used in defining conic sections, the four types of which are the circle, ellipse, parabola, and hyperbola. In addition, two foci are used to define the Cassini oval and the Cartesian oval, and more than two foci are used in defining an n-ellipse.
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In mathematics, the Jacobi elliptic functions are a set of basic elliptic functions, and auxiliary theta functions, that are of historical importance. They are found in the description of the motion of a pendulum (see also pendulum (mathematics)), as well as in the design of the electronic elliptic filters. While trigonometric functions are defined with reference to a circle, the Jacobi elliptic functions are a generalization which refer to other conic sections, the ellipse in particular. The relation to trigonometric functions is contained in the notation, for example, by the matching notation sn for sin.
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The height of the shell attains 32 mm, its diameter 39 mm. This species is allied to Trochus maculatus Linnaeus, 1758 but differs in the following characters: the form is more conic, the body whorl is less convex and less elevated. The spiral lirae on the inferior part of the body whorl are less conspicuous. The longitudinal folds are strongly developed, rendering the periphery dentate ; Trochus incarnatus Philippi, 1846 (a taxon inquirendum) differs from this species in being less conical, smaller, more elongate, with fewer lirae on thebase (7 or 8 instead of 12), etc.
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Though the instrument is slightly conic on the outside, its perforation is cylindrical. The kuisi bunsi has five tone holes, but only four of them are used when performing: the lower tone hole is rarely used, but when used, the upper tone hole is closed with wax. The lower tone hole of the kuisi sigi is rarely used. The instrument's head, called a fotuto in Spanish, is made with bee wax mixed with charcoal powder to prevent the wax melting in high temperatures, which also gives the head it a characteristic black color.
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The small shell measures 2.1 mm. It is umbilicated, elongate-ovate conic, semitransparent, polished. The 2½ whorls of the protoconch are moderately large, helicoid, elevated, about one-fifth immersed in the first of the succeeding whorls and having their axis at a right angle to them. The five whorls of the teleoconch are flattened, angulated at the periphery and weakly shouldered at the summit; the latter falls somewhat anterior to the periphery of the preceding whorl and lends to it a somewhat constricted appearance at the well-impressed suture.
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By Wedderburn's theorem every finite skewfield is a field and an automorphism of order two (other than the identity) can only exist in a finite field whose order is a square. These facts help to simplify the general situation for finite Desarguesian planes. We have: If is a polarity of the finite Desarguesian projective plane where for some prime , then the number of absolute points of is if is orthogonal or if is unitary. In the orthogonal case, the absolute points lie on a conic if is odd or form a line if .
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The leaves are needle-like, light green, 2–4 cm long which turn bright yellow before they fall in the autumn, leaving the pale yellow-buff shoots bare until the next spring. The cones are erect, ovoid-conic, 2–6 cm long, with 10-90 erect or slightly incurved (not reflexed) seed scales; they are green variably flushed red when immature, turning brown and opening to release the seeds when mature, 4–6 months after pollination. The old cones commonly remain on the tree for many years, turning dull grey-black.
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Especially during evening events the combination of these elements create an inimitable sign symbolizing the city of Konya. The semi transparent screen façade renders the characteristic conic shape and allows laser shows and the projection of images from outside and the inside as well. The stadium is designed as a one-tier- stadium with a formidable east and west stand – both have more than 60 rows – and will achieve a great atmosphere for the spectators, for instance the fantastic view for the VIP and the media from the west to the east stand.
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He also made discoveries about projective harmonic conjugates; relating these to the poles and polar lines associated with conic sections. He developed the concept of parallel lines meeting at a point at infinity and defined the circular points at infinity that are on every circle of the plane. These discoveries led to the principle of duality, and the principle of continuity and also aided in the development of complex numbers. As a military engineer, he served in Napoleon's campaign against the Russian Empire in 1812, in which he was captured and held prisoner until 1814.
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The equations of the circle and the other conic sections--ellipses, parabolas, and hyperbolas--are quadratic equations in two variables. Given the cosine or sine of an angle, finding the cosine or sine of the angle that is half as large involves solving a quadratic equation. The process of simplifying expressions involving the square root of an expression involving the square root of another expression involves finding the two solutions of a quadratic equation. Descartes' theorem states that for every four kissing (mutually tangent) circles, their radii satisfy a particular quadratic equation.
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The intersections of the extended opposite sides of inscribed hexagon ABCDEF lie on the blue Pascal line MNP. The hexagon's extended sides are in gray and red. Pascal's theorem states that if six arbitrary points are chosen on a conic section (i.e., ellipse, parabola or hyperbola) and joined by line segments in any order to form a hexagon, then the three pairs of opposite sides of the hexagon (extended if necessary) meet in three points which lie on a straight line, called the Pascal line of the hexagon.
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Foliage The shoots are brown to gray-brown, smooth, though not as smooth as fir shoots, and finely pubescent with scattered short hairs. The buds are a distinctive narrow conic shape, long, with red-brown bud scales. The leaves are spirally arranged but slightly twisted at the base to be upswept above the shoot, needle-like, long, gray-green to blue-green above with a single broad stomatal patch, and with two whitish stomatal bands below. The male (pollen) cones are long, and are typically restricted to, or more abundant on, lower branches.
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In analytic geometry, any equation involving the coordinates specifies a subset of the plane, namely the solution set for the equation, or locus. For example, the equation y = x corresponds to the set of all the points on the plane whose x-coordinate and y-coordinate are equal. These points form a line, and y = x is said to be the equation for this line. In general, linear equations involving x and y specify lines, quadratic equations specify conic sections, and more complicated equations describe more complicated figures.
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Leaf; under side (left) and upper side (right) It is a medium-sized deciduous tree growing to 10–15 m tall with a stout trunk up to 60 cm in diameter, and grey bark. The crown is columnar or conic in young trees, becoming rounded with age, with branches angled upwards. The leaves are green above, and densely hairy with white hairs beneath. 7–12 cm long and 5–8 cm broad, the leaves are lobed, with six to nine oval lobes on each side of the leaf.
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It is a large evergreen coniferous tree reaching tall, exceptionally with a trunk up to in diameter. It has a conic crown with level branches and drooping branchlets. The leaves are needle-like, mostly long, occasionally up to long, slender ( thick), borne singly on long shoots, and in dense clusters of 20–30 on short shoots; they vary from bright green to glaucous blue-green in colour. The female cones are barrel-shaped, long and broad, and disintegrate when mature (in 12 months) to release the winged seeds.
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The shell is sinistral, ovate-conic, thin but strong, nearly smooth, brilliantly glossy. The shell has 5.5 whorls. The embryonic whorls are burnt sienna brown (weathering to whitish in adult shells), or sometimes there is a light median zone. The last whorl has either a uniform blackish chestnut, or a chestnut peripheral band and baso-columellar patch on a yellow ground, or like the last but with a green band midway between periphery and suture, or with sutural and peripheral bands and a baso- columellar patch of yellow on a chestnut ground.
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Robert Catesby Taliaferro (1907–1989) was an American mathematician, science historian, classical philologist, philosopher, and translator of ancient Greek and Latin works into English. An Episcopalian from an old Virginia family, he taught in the mathematics department of the University of Notre Dame. He is cited as R. Catesby Taliaferro or R. C. Taliaferro. He translated from Greek and Latin into English: Ptolemy's Almagest, a 2nd-century book on astronomy, the 13 books of Euclid's Elements, Apollonius' works on conic sections, and some works of Plato (Timaios, Critias), and St. Augustine (On Music).
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Lambert did not give names to any of his projections but they are now known as: # Lambert conformal conic # Transverse Mercator # Lambert azimuthal equal area # Lagrange projection # Lambert cylindrical equal area # Transverse cylindrical equal area # Lambert conical equal area The first three of these are of great importance.Corresponding to the Lambert azimuthal equal-area projection, there is a Lambert zenithal equal-area projection. The Times Atlas of the World (1967), Boston: Houghton Mifflin, Plate 3 et passim. Further details may be found at map projections and in several texts.
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The resin was used in the manufacture of pitch in the past (before the use of petrochemicals); the scientific name Picea derives from Latin "pitch pine" (referring to Scots pine), from , an adjective from "pitch". Native Americans in North America use the thin, pliable roots of some species for weaving baskets and for sewing together pieces of birch bark for canoes. See also Kiidk'yaas for an unusual golden Sitka Spruce sacred to the Haida people. Spruces are popular ornamental trees in horticulture, admired for their evergreen, symmetrical narrow-conic growth habit.
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Curves on the graph can be traced by a cursor, where local maximum, local minimum, and intersections of the curves can be solved by a graph solver tool. Conics having their axes parallel to x-axis or y-axis can be plotted through a separate application. This means that the calculators cannot plot other conic/quadratic equations Ax^2+Bxy+Cy^2+Dx+Ey+F=0 where B is not equal to 0. The Algebra FX series cannot plot any implicit function of two variables, while the Texas Instrument's TI-89 series can.
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In 1920 he taught at a technical institute in Turin and subsequently at the Scientific High School "Galileo Ferraris", also in Turin. Immediately after World War I, Artom produced the scientific publications which would gain him the 1930 Mathesis award for a history of conic sections in elementary mathematics. Almost resolved to a more sustained effort in scientific research, he could not however obtain a professorship due to political reasons, as he was not willing to join the National Fascist Party. Artom hence committed himself to linguistic studies.
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This frames the entrance and is shaped on either side in pillars, and above and below is shaped as a flat portal and a threshold respectively. The two facade columns of the tomb which form the appearance of the tomb in width and depth axis are almost of the same shape. The capitals appear to be composed of simple square or rectangular shapes. The conic pedestals of the two front columns are of the same level as the threshold of the front porch, but are on a different floor level from the main porch.
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A cylindric section in which the intersecting plane intersects and is perpendicular to all the elements of the cylinder is called a '. If a right section of a cylinder is a circle then the cylinder is a circular cylinder. In more generality, if a right section of a cylinder is a conic section (parabola, ellipse, hyperbola) then the solid cylinder is said to be parabolic, elliptic and hyperbolic respectively. Cylindric sections of a right circular cylinder For a right circular cylinder, there are several ways in which planes can meet a cylinder.
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The shell is greenish brown and roughly an equilateral triangle in profile with a slightly wavy thickened edge on the bottom of the whorl and sculpture consisting of fine diagonal spiral ridges. The single most striking feature is a brilliant spot of reddish-orange at the base of the umbilical pit which is bordered by a dark brown to black outer edge. Average height is 55 mm, and average diameter is 65 mm. Drawing with two views of a shell of Uvanilla olivacea The acute, imperforate shell has a conic shape.
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Side view Dexia rustica can reach a body length of and a wingspan of 16–24 mm.J.K. Lindsey Commanster These small tachinids have generally a black thorax, with grayish yellow pruinosity. Four longitudinal black vittae appear on dorsum,Chun-Tian Zhang, Xiao-Lin Chen A review of the genus Dexia Meigen in the Palearctic and Oriental Regions Diptera Tachinidae in Zootaxa · December 2010 Abdomen appears greyish-brown or reddish, with a darker longitudinal dorsal marking, more or less evident. It is cylindric- conic, with two setae among each segment.
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The other oval, if it exists, does not contain any real inflection point and appears either as an oval or as two infinite branches. Like for conic sections, a line cuts this oval at, at most, two points. A non-singular plane cubic defines an elliptic curve, over any field K for which it has a point defined. Elliptic curves are now normally studied in some variant of Weierstrass's elliptic functions, defining a quadratic extension of the field of rational functions made by extracting the square root of a cubic.
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The small shell is elongate-conic, rather stout and semitranslucent. The nuclear whorls are small, two and one-half, forming: a depressed helicoid spire, whose axis is at right angles to that of the succeeding turns, in the first of which it is about one-fourth immersed. Post- nuclear whorls are flattened, moderately contracted at the sutures and slightly shouldered at the summit, marked by very strong, lamellar, somewhat retractive axial ribs, of which 14 occur upon all of the whorls. The termination of these ribs form cusps at the summits.
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229 It was realised that the theorems that do apply to projective geometry are simpler statements. For example, the different conic sections are all equivalent in (complex) projective geometry, and some theorems about circles can be considered as special cases of these general theorems. During the early 19th century the work of Jean-Victor Poncelet, Lazare Carnot and others established projective geometry as an independent field of mathematics . Its rigorous foundations were addressed by Karl von Staudt and perfected by Italians Giuseppe Peano, Mario Pieri, Alessandro Padoa and Gino Fano during the late 19th century.
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The first step was a precise characterization of the error in the main mirror. Working backwards from images of point sources, astronomers determined that the conic constant of the mirror as built was , instead of the intended . The same number was also derived by analyzing the null corrector used by Perkin-Elmer to figure the mirror, as well as by analyzing interferograms obtained during ground testing of the mirror. COSTAR being removed in 2009 Because of the way the HST's instruments were designed, two different sets of correctors were required.
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Hypatia wrote a commentary on Apollonius of Perga's treatise on conic sections, but this commentary is no longer extant. Hypatia wrote a commentary on Diophantus's thirteen-volume Arithmetica, which had been written sometime around the year 250 AD. It set out more than 100 mathematical problems, for which solutions are proposed using algebra. For centuries, scholars believed that this commentary had been lost. Only volumes one through six of the Arithmetica have survived in the original Greek, but at least four additional volumes have been preserved in an Arabic translation produced around the year 860.
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Recent authors have recognized this genus as nonmonophyetic, rejecting that the genus is a natural grouping. Two unnamed groups are distinguished by accessory tooth plates, which are either very elongated and bearing molar-like teeth, or are oval shaped or subtriangular and bearing acicular (needle-like) or conic teeth. A. jatius lacks these tooth plates, but has been included in this genus based on its adipose fin and lateral line. The recognition of Arenarius as a junior synonym of Arius is tentative and needs to be further investigated.
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He could also create a gravitational force field around him capable of protecting him from any concussive force up to and including a small nuclear weapon. On a large scale Graviton could exert his gravitational control over a maximum distance of from his body. Thus, the maximum volume of matter he could influence at once is . He once exercised this control by lifting into the air an inverted conic frustum-shaped land mass whose uppermost area was across, and causing it to fly as though it were a blimp.
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Jakob Steiner had proposed Steiner's conic problem of enumerating the number of conic sections tangent to each of five given conics, and had answered it incorrectly. Chasles developed a theory of characteristics that enabled the correct enumeration of the conics (there are 3264) (see enumerative geometry). He established several important theorems (all called Chasles's theorem). In kinematics, Chasles's description of a Euclidean motion in space as screw displacement was seminal to the development of the theories of dynamics of rigid bodies. Chasles was elected a Foreign Honorary Member of the American Academy of Arts and Sciences in 1864. In 1865 he was awarded the Copley Medal. As described in A Treasury of Deception, by Michael Farquhar (Peguin Books, 2005), between 1861 and 1869 Chasles purchased some of the 27,000 forged letters from Frenchman Denis Vrain-Lucas. Included in this trove were letters from Alexander the Great to Aristotle, from Cleopatra to Julius Caesar, and from Mary Magdalene to a revived Lazarus, all in a fake medieval French. In 2004, the journal Critical Inquiry published a recently "discovered" 1871 letter written by Vrain-Lucas (from prison) to Chasles, conveying Vrain-Lucas's perspective on these events,Ken Alder, "History's Greatest Forger: Science, Fiction, and Fraud Along the Seine," Critical Inquiry 30 (Summer 2004): 704–716.
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The Inverclyde Group is present in a couple of outliers immediately north of the Highland Boundary Fault to the east and west of Loch Lomond. The eastern outlier forms the ground just to the north of Conic Hill and is assigned to the Kinnesswood Formation which consists of sandstones, often conglomeratic at their base, together with mudstones and cornstones (nodular carbonates). The Ballaggan Formation which includes mudstones and siltstones within which are thin beds (or sometimes just nodules) of ferroan dolomite, traditionally referred to as ‘cementstones’, is represented by a very small inlier on the park's southwestern boundary.
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Book III contains 56 propositions. Apollonius claims original discovery for theorems "of use for the construction of solid loci ... the three-line and four-line locus ...." The locus of a conic section is the section. The three-line locus problem (as stated by Taliafero's appendix to Book III) finds "the locus of points whose distances from three given fixed straight lines ... are such that the square of one of the distances is always in a constant ratio to the rectangle contained by the other two distances." This is the proof of the application of areas resulting in the parabola.
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Book VI, known only through translation from the Arabic, contains 33 propositions, the least of any book. It also has large lacunae, or gaps in the text, due to damage or corruption in the previous texts. The topic is relatively clear and uncontroversial. Preface 1 states that it is “equal and similar sections of cones.” Apollonius extends the concepts of congruence and similarity presented by Euclid for more elementary figures, such as triangles, quadrilaterals, to conic sections. Preface 6 mentions “sections and segments” that are “equal and unequal” as well as “similar and dissimilar,” and adds some constructional information.
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However, the introduction of greenhouse plantations has made them available throughout the year. Padrón peppers are small, with an elongated, conic shape. The taste is mild, but some exemplars can be quite hot, which property has given rise to the popular Galician aphorism Os pementos de Padrón, uns pican e outros non ("Padrón peppers, some are hot, some are not"). Typically, there is no way of determining whether a given pepper will be hot or mild, short of actually eating it, though some maintain that smelling each cooked Padrón for spice prior to eating is a good indicator.
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Foliage, mature seed cone, and (center) old pollen cone The bark is thin and scaly, flaking off in small, circular plates across. The crown is broad conic in young trees, becoming cylindric in older trees; old trees may not have branches lower than . The shoots are very pale buff-brown, almost white, and glabrous (hairless), but with prominent pulvini. The leaves are stiff, sharp, and needle-like, 15–25 mm long, flattened in cross-section, dark glaucous blue-green above with two or three thin lines of stomata, and blue-white below with two dense bands of stomata.
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Precalculus prepares students for calculus somewhat differently from the way that pre-algebra prepares students for algebra. While pre-algebra often has extensive coverage of basic algebraic concepts, precalculus courses might see only small amounts of calculus concepts, if at all, and often involves covering algebraic topics that might not have been given attention in earlier algebra courses. Some precalculus courses might differ with others in terms of content. For example, an honors- level course might spend more time on conic sections, Euclidean vectors, and other topics needed for calculus, used in fields such as medicine or engineering.
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Circle (e=0), ellipse (e=1/2), parabola (e=1) and hyperbola (e=2) with fixed focus F and directrix (e=∞). Alternatively, one can define a conic section purely in terms of plane geometry: it is the locus of all points whose distance to a fixed point (called the focus) is a constant multiple (called the eccentricity ) of the distance from to a fixed line (called the directrix). For we obtain an ellipse, for a parabola, and for a hyperbola. A circle is a limiting case and is not defined by a focus and directrix in the Euclidean plane.
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It is believed that the first definition of a conic section was given by Menaechmus (died 320 BCE) as part of his solution of the Delian problem (Duplicating the cube).According to Plutarch this solution was rejected by Plato on the grounds that it could not be achieved using only straightedge and compass, however this interpretation of Plutarch's statement has come under criticism. His work did not survive, not even the names he used for these curves, and is only known through secondary accounts. The definition used at that time differs from the one commonly used today.
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Currently, there are more than twenty MC battles taking place in Brasília, which function as tournaments where the participants are judged by the public (and, sometimes, also by judges) who evaluate their ability in constructing freestyle rhymes and verses. It is uncertain to specify when exactly Brasília's MC battles first initiated, but the growth in their popularity is quite noticeable. In 2010, there were three regular MC battles, such as the Calango Pensante event, which took place monthly at the Conic mall. Nowadays, there are more than twenty battles and the majority occur on a weekly basis.
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The television coverage of the impeachment vote on 31 August 2016, was watched by 35.1 million viewers in Brazil, according to GfK research. Protests supporting the impeachment process and against Rousseff's government occurred on March 13 in all states of the country, in over 300 cities, gathering over 3.6 million people. Rousseff's impeachment was supported by the Industrial Federation of the State of São Paulo, after internal opinion surveys. In December 2015, Rio de Janeiro's Industrial Federation also began supporting the impeachment while Brazil's National Council of Christian Churches (CONIC) and Episcopal Conference (CNBB) positioned themselves against the impeachment.
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Sangallo's plan (1513), of which a large wooden model still exists, looks to both these predecessors. He realized the value of both the coffering at the Pantheon and the outer stone ribs at Florence Cathedral. He strengthened and extended the peristyle of Bramante into a series of arched and ordered openings around the base, with a second such arcade set back in a tier above the first. In his hands, the rather delicate form of the lantern, based closely on that in Florence, became a massive structure, surrounded by a projecting base, a peristyle and surmounted by a spire of conic form.
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The bifilar dial was invented in April 1922 by the mathematician and maths teacher, Hugo Michnik, from Beuthen, Upper Silesia. He studied the horizontal dial- starting on a conventional XYZ cartesian framework and building up a general projection which he states was an exceptional case of a Steiner transformation. He related the trace of the sun to conic sections and the angle on the dial-plate to the hour angle and the calculation of local apparent time, using conventional hours and the historic Italian and Babylonian hours. He refers in the paper, to a previous publication on the theory of sundials in 1914.
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Jean-Victor Poncelet (1788−1867) author of the first text on projective geometry, Traité des propriétés projectives des figures, was a synthetic geometer who systematically developed the theory of poles and polars with respect to a conic. Poncelet maintained that the principle of duality was a consequence of the theory of poles and polars. Julius Plücker (1801−1868) is credited with extending the concept of duality to three and higher dimensional projective spaces. Poncelet and Gergonne started out as earnest but friendly rivals presenting their different points of view and techniques in papers appearing in Annales de Gergonne.
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Typical requirements for grinding and polishing a curved mirror, for example, require the surface to be within a fraction of a wavelength of light of a particular conic shape. Many modern "telescopes" actually consist of arrays of telescopes working together to provide higher resolution through aperture synthesis. Large telescopes are housed in domes, both to protect them from the weather and to stabilize the environmental conditions. For example, if the temperature is different from one side of the telescope to the other, the shape of the structure changes, due to thermal expansion pushing optical elements out of position.
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Two kilometers upstream from El Naranjo exists a series of pools and cascades, such as El Salto and El Meco, which are 70-m and 35-m high, respectively; both sites are inhabited by H. pratinus." "This species is distinguished by predorsal contour steep and flat, and a concavity before eye; prominent forehead that develops a nuchal hump in adult males. Dorsal and ventral contours are conic, straight to moderately convex, making intersection with caudal peduncle conspicuous. Also distinguished using the following combination characters: distance from anal fin origin to hypural base (mean 36%, SD 1%).
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The special perpendicular is employed to compute the volume of a pyramid (p 35), an equation on skew lines that reduces to zero when they are coplanar, a property of a spherical triangle, and the coincidence of the perpendiculars in a tetrahedron. Chapter four describes equations of geometric figures: line, plane, circle, sphere. The definition of a conic section is taken from Kelland and Tait: "the locus of a point which move so that its distance from a fixed point bears a constant ratio to its distance from a fixed straight line." Ellipse, hyperbola, and parabola are then illustrated.
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The broadly conic shell is pale yellow, with a broad dark wax yellow band, which extends over a little more than one-half the distance from the middle of the whorls to the summit, between the sutures. A secondary of the same color extends from a little posterior to the periphery to the middle of the base. Its length measures 5.8 mm. The 2½ whorls of the protoconch are small and form a depressed helicoid spire, the axis of which is at right angles to that of the succeeding turns, in the first of which they are very slightly immersed.
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The elongate-conic shell has a wax yellow color, with two yellowish-brown spiral bands The posterior one of which encircles the turns a little above the periphery, while the anterior one, which is a little wider, is immediately posterior to it, the two being separated by a space about as wide as the posterior band. Its length attains 8.5 mm. The whorls of the protoconch are decollated in the type specimen. The 8½ remaining whorls of the teleoconch are very slightly rounded, moderately contracted at the periphery, and closely appressed to the preceding turn at the summit.
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2a, the optical elements are oriented so that S′1 and S′2 are in line with the observer, and the resulting interference pattern consists of circles centered on the normal to M1 and M'2. If, as in Fig. 2b, M1 and M′2 are tilted with respect to each other, the interference fringes will generally take the shape of conic sections (hyperbolas), but if M′1 and M′2 overlap, the fringes near the axis will be straight, parallel, and equally spaced. If S is an extended source rather than a point source as illustrated, the fringes of Fig.
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After finishing school in 1810, Cauchy accepted a job as a junior engineer in Cherbourg, where Napoleon intended to build a naval base. Here Augustin-Louis stayed for three years, and was assigned the Ourcq Canal project and the Saint-Cloud Bridge project, and worked at the Harbor of Cherbourg. Although he had an extremely busy managerial job, he still found time to prepare three mathematical manuscripts, which he submitted to the Première Classe (First Class) of the Institut de France. Cauchy's first two manuscripts (on polyhedra) were accepted; the third one (on directrices of conic sections) was rejected.
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The result on the Legendre symbol amounts to the formula for the number of points on a conic section that is a projective line over the field of p elements. A paper of André Weil from 1949 very much revived the subject. Indeed, through the Hasse–Davenport relation of the late 20th century, the formal properties of powers of Gauss sums had become current once more. As well as pointing out the possibility of writing down local zeta-functions for diagonal hypersurfaces by means of general Jacobi sums, Weil (1952) demonstrated the properties of Jacobi sums as Hecke characters.
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These zones use the Lambert conformal conic projection, because it is good at maintaining accuracy along an east–west axis, due to the projection cone intersecting the earth's surface along two lines of latitude. Zones that are long in the north–south direction use the transverse Mercator projection because it is better at maintaining accuracy along a north–south axis, due to the circumference of the projection cylinder being oriented along a meridian of longitude. The panhandle of Alaska, whose maximum dimension is on a diagonal, uses an Oblique Mercator projection, which minimizes the combined error in the X and Y directions.
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Illustratiom from De ichnographica campi published in Acta Eruditorum, 1763 La perspective affranchie de l'embarras du plan géometral, French edition, 1759 Lambert was the first to introduce hyperbolic functions into trigonometry. Also, he made conjectures regarding non-Euclidean space. Lambert is credited with the first proof that π is irrational by using a generalized continued fraction for the function tan x. Euler believed the conjecture but could not prove that π was irrational, and it is speculated that Aryabhata also believed this, in 500 CE. Lambert also devised theorems regarding conic sections that made the calculation of the orbits of comets simpler.
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After a rudimentary education at the Revd Charles Udal's school in Garsdale, Dawson worked until he was about twenty as a shepherd on his father's freehold, developing an interest in mathematics in his spare time with the aid of books that he bought with the profits from stocking knitting or borrowed from his elder brother, who had become an excise officer. Despite being entirely self-taught he worked up his own system of conic sections and began to establish himself as a teacher of mathematics, often spending two or three months at a time in the houses of his pupils.
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The axis of a cone is the straight line (if any), passing through the apex, about which the base (and the whole cone) has a circular symmetry. In common usage in elementary geometry, cones are assumed to be right circular, where circular means that the base is a circle and right means that the axis passes through the centre of the base at right angles to its plane. If the cone is right circular the intersection of a plane with the lateral surface is a conic section. In general, however, the base may be any shapeGrünbaum, Convex Polytopes, second edition, p. 23.
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Phaeocollybia is defined as mushrooms, with a glutinous or moist or sometimes dry and innately scaly, conic, umbonate cap, a rooting, cartilaginous to wiry stipe, generally lacking a visible veil or cortina or with faint traces, and spores which are brown in deposit. The spores are ornamented but will lack a germ pore or plage. The most distinctive feature microscopically is the presence of tibiiformIn the shape of a tibia bone, that is, with a long narrow neck with an apex that is swollen into a knob, like a tibia. cystidia or branches on the mycelium and mycorrhizal sheaths.
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In 1704, appeared his Treatise on Fluxions, or an Introduction to Mathematical Philosophy, London, the first English work explaining Isaac Newton's method of infinitesimals. After an introduction on conic sections with concise proofs, Hayes applied Newton's method systematically, first to obtain the tangents of curves, then their areas, and lastly to problems of maxima and minima. His preface shows he was well read in mathematical literature. In 1710 he printed a pamphlet, New and Easy Method to find out the Longitude; and in 1723 The Moon, a Philosophical Dialogue, arguing that she is not opaque, but has some light of her own.
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The cones are broad cylindric-conic, 9–16 cm long and 3 cm broad, green when young, maturing buff-brown and opening to 5–6 cm broad 5–7 months after pollination; the scales are stiff and smoothly rounded. Morinda spruce is a popular ornamental tree in large gardens in western Europe for its attractive pendulous branchlets. It is also grown to a small extent in forestry for timber and paper production, though its slower growth compared to Norway spruce reduces its importance outside of its native range. The name morinda derives from the tree's name in Nepali.
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Charles Smith (b Huntingdon, 11 May 1844; d Cambridge 13 November 1916) was a 20th-century British academic.Amongst others he wrote "An Elementary Treatise on Conic Sections", 1882; "An Elementary Treatise on Solid Geometry", 1884; "Elementary Algebra", 1886; "Treatise on Algebra", 1887; "Arithmetic", 1891; "Geometrical Conics" 1894; and "Euclid" 1901 > British Library web site accessed 17:48 GMT Tuesday 31 July 2018 Smith was educated at Sidney Sussex College, Cambridge. He became a Fellow of Sidney Sussex in 1868; Tutor in 1875; and Master in 1890. He was Vice-Chancellor of the University of Cambridge from 1895 to 1897.
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142–146 With respect to the beginnings of projective geometry, Kepler introduced the idea of continuous change of a mathematical entity in this work. He argued that if a focus of a conic section were allowed to move along the line joining the foci, the geometric form would morph or degenerate, one into another. In this way, an ellipse becomes a parabola when a focus moves toward infinity, and when two foci of an ellipse merge into one another, a circle is formed. As the foci of a hyperbola merge into one another, the hyperbola becomes a pair of straight lines.
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Relationships not readily amenable to pictorial solutions were beyond his grasp; however, his repertory of pictorial solutions came from a pool of complex geometric solutions generally not known (or required) today. One well-known exception is the indispensable Pythagorean Theorem, even now represented by a right triangle with squares on its sides illustrating an expression such as a2 \+ b2 = c2. The Greek geometers called those terms “the square on AB,” etc. Similarly, the area of a rectangle formed by AB and CD was "the rectangle on AB and CD." These concepts gave the Greek geometers algebraic access to linear functions and quadratic functions, which latter the conic sections are.
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It is a medium-sized evergreen conifer growing to tall, exceptionally to tall, with a trunk up to across, and a very narrow conic crown. The bark on young trees is smooth, gray, and with resin blisters, becoming rough and fissured or scaly on old trees. The leaves are flat and needle-like, long, glaucous green above with a broad stripe of stomata, and two blue-white stomatal bands below; the fresh leaf scars are reddish. They are arranged spirally on the shoot, but with the leaf bases twisted to be arranged to the sides of and above the shoot, with few or none below the shoot.
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Triple-pour beer tower Conic "Beer Giraffe" A beer tower (also known as a portable beer tap, a tabletop beer dispenser, a triton dispenser or a giraffe) is a beer dispensing device, sometimes found in bars, pubs and restaurants. The idea behind beer towers is that several patrons in a group can serve themselves the amount of beer they want without having to order individually. The device comes in a variety of sizes, most often double to triple the size of standard beer pitchers that hold around of beer. Early versions came in the shape of a four-foot tall plastic cylinder attached to a beer tap at the bottom.
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Collaborating on the teaching of conic sections, Rajagopal and Vaniyambadi Rajagopala Srinivasaraghavan wrote a textbook, An Introduction to Analyical Conics, that was published in 1955 by Oxford University Press in India. A reviewer noted "a pleasing feature is the frequent reference to the history of the subject", and "the authors pursue the theory in great detail, proving a large number of subsidiary results."E.J.F. Primrose (1957) "Review: An introduction to analytical conics by Rajagopal & Srinivasaraghvan", The Mathematical Gazette 41 Rajagopal became Director of the Ramanujan Institute for Advanced Study in Mathematics in 1955. He helped the Institute to become India's leading mathematics research centre.
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Four abreast cabin seating of a CRJ-1000 NextGen The flight deck of a CRJ-1000 NextGen During 2007, Bombardier launched the CRJ900 NextGen to replace the initial version. Its improvements and conic nozzle enhances fuel economy by 5.5%. The new model has improved economics and a new cabin common to the CRJ700 NextGen and CRJ1000 NextGen. Mesaba Aviation (now Endeavor Air), operating at the time as Northwest Airlink (now Delta Connection), was the launch customer, and remains the largest operator of the CRJ900 NextGen. The Endeavor fleet of CRJ900 NextGen aircraft are configured in a two class seating configuration, with 12 first class seats and 64 coach seats.
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Another important contribution Thabit made to geometry was his generalization of the Pythagorean theorem, which he extended from special right triangles to all triangles in general, along with a general proof. Ibrahim ibn Sinan ibn Thabit (born 908), who introduced a method of integration more general than that of Archimedes, and al-Quhi (born 940) were leading figures in a revival and continuation of Greek higher geometry in the Islamic world. These mathematicians, and in particular Ibn al- Haytham, studied optics and investigated the optical properties of mirrors made from conic sections. Astronomy, time-keeping and geography provided other motivations for geometrical and trigonometrical research.
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A point (x,y,z) of the contour line of an implicit surface with equation f(x,y,z)=0 and parallel projection with direction \vec v has to fulfill the condition g(x,y,z)= abla f(x,y,z)\cdot \vec v=0, because \vec v has to be a tangent vector, which means any contour point is a point of the intersection curve of the two implicit surfaces : f(x,y,z)=0 ,\ g(x,y,z)=0. For quadrics, g is always a linear function. Hence the contour line of a quadric is always a plane section (i.e. a conic section).
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In geometry, trope is an archaic term for a singular (meaning special) tangent space of a variety, often a quartic surface. The term may have been introduced by , who defined it as "the reciprocal term to node". It is not easy to give a precise definition, because the term is used mainly in older books and papers on algebraic geometry, whose definitions are vague and different, and use archaic terminology. The term trope is used in the theory of quartic surfaces in projective space, where it is sometimes defined as a tangent space meeting the quartic surface in a conic; for example Kummer's surface has 16 tropes.
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The ancient Greeks classified constructions into three major categories, depending on the complexity of the tools required for their solution. If a construction used only a straightedge and compass, it was called planar; if it also required one or more conic sections (other than the circle), then it was called solid; the third category included all constructions that did not fall into either of the other two categories.T.L. Heath, "A History of Greek Mathematics, Volume I" This categorization meshes nicely with the modern algebraic point of view. A complex number that can be expressed using only the field operations and square roots (as described above) has a planar construction.
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Similarly, tangency to a given line L (tangency is intersection with multiplicity two) is one quadratic condition, so determined a quadric in P5. However the linear system of divisors consisting of all such quadrics is not without a base locus. In fact each such quadric contains the Veronese surface, which parametrizes the conics :(aX + bY + cZ)2 = 0 called 'double lines'. This is because a double line intersects every line in the plane, since lines in the projective plane intersect, with multiplicity two because it is doubled, and thus satisfies the same intersection condition (intersection of multiplicity two) as a nondegenerate conic that is tangent to the line.
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Further unification occurs in the complex projective plane CP2: the non-degenerate conics cannot be distinguished from one another, since any can be taken to any other by a projective linear transformation. It can be proven that in CP2, two conic sections have four points in common (if one accounts for multiplicity), so there are between 1 and 4 intersection points. The intersection possibilities are: four distinct points, two singular points and one double point, two double points, one singular point and one with multiplicity 3, one point with multiplicity 4. If any intersection point has multiplicity > 1, the two curves are said to be tangent.
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In the early 1980s, "[i]conic punk fanzines like Flipside, which could make or break [band] reputations, pronounced them [Discharge] "fucking great." Treble zine called it one of the top ten essential hardcore albums, along with Black Flag's Damaged and the Dead Kennedys Fresh Fruit for Rotting Vegetables. Treble zine states that the music on HNSNSN was "much, much heavier" than previous punk and states that it influenced "punk rock, [and]... metal circles" with its "raw and intense" sound. Anthrax guitarist Scott Ian stated in 2015 that "You put on... Hear Nothing, See Nothing, Say Nothing album now, and it’s still as heavy and brutal as anything out there.
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In other cases, the hour-lines are not spaced evenly, even though the shadow rotates uniformly. If the gnomon is not aligned with the celestial poles, even its shadow will not rotate uniformly, and the hour lines must be corrected accordingly. The rays of light that graze the tip of a gnomon, or which pass through a small hole, or reflect from a small mirror, trace out a cone aligned with the celestial poles. The corresponding light-spot or shadow-tip, if it falls onto a flat surface, will trace out a conic section, such as a hyperbola, ellipse or (at the North or South Poles) a circle.
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It is also possible to describe all the conic sections as loci of points that are equidistant from a single focus and a single, circular directrix. For the ellipse, both the focus and the center of the directrix circle have finite coordinates and the radius of the directrix circle is greater than the distance between the center of this circle and the focus; thus, the focus is inside the directrix circle. The ellipse thus generated has its second focus at the center of the directrix circle, and the ellipse lies entirely within the circle. For the parabola, the center of the directrix moves to the point at infinity (see projective geometry).
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In algebraic geometry, the conic sections in the projective plane form a linear system of dimension five, as one sees by counting the constants in the degree two equations. The condition to pass through a given point P imposes a single linear condition, so that conics C through P form a linear system of dimension 4. Other types of condition that are of interest include tangency to a given line L. In the most elementary treatments a linear system appears in the form of equations :\lambda C + \mu C' = 0\ with λ and μ unknown scalars, not both zero. Here C and C′ are given conics.
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However, Alex Au and 5 other directors were resigned and replaced by directors that were nominated by Sin King shortly after the takeover. A scandal that involves false accounting as well as illegal withdrew of the capital of the listed company was also reveal in 1984–85, with 2 of the resigned directors Tam Chun Shing () and Lam Chun Kiu (), as well as 7 managers were arrested. It was also reported that Alex Au was fled to Taiwan in 1984, who refused to refurbish the loan of Honic from Conic. Au also involved in a kidnapping crime in 1985 which he was reportly kidnapped his new business partner.
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The parabola is the locus of points in that plane that are equidistant from both the directrix and the focus. Another description of a parabola is as a conic section, created from the intersection of a right circular conical surface and a plane parallel to another plane that is tangential to the conical surface. The line perpendicular to the directrix and passing through the focus (that is, the line that splits the parabola through the middle) is called the "axis of symmetry". The point where the parabola intersects its axis of symmetry is called the "vertex" and is the point where the parabola is most sharply curved.
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European larch morphology features from book: Prof. Dr. Otto Wilhelm Thomé Flora von Deutschland, Österreich und der Schweiz, 1885, Gera, Germany. Larix decidua is a medium- size to large deciduous coniferous tree reaching 25–45 m tall, with a trunk up to 1 m diameter (exceptionally, to 53.8 m tall and 3.5 m diameter). The crown is conic when young, becoming broad with age; the main branches are level to upswept, with the side branches often pendulous. The shoots are dimorphic, with growth divided into long shoots (typically 10–50 cm long) and bearing several buds, and short shoots only 1–2 mm long with only a single bud.
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Communion-table, sanctuary and seats for celebrants are located in the northern part of the church. Room above sacristy holds seats, reserved in the past for patrons, nobles. There is wooden Classicist altar from year 1800Archives of The Monuments Board of the Slovak Republic, Research Report from 18 June 1954 with modern Statue of the Sacred Heart located in the right part of triumphal arch and preserved original Classicist pulpit with conic tribune and canopy on the left. The Statue of Immaculate Heart of Mary on the left and Statue of the Sacred Heart on the right decorate the facade of the yellow-white building.
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Tree in habitat Larix griffithii, the Sikkim larch, is a species of larch, native to the eastern Himalaya in eastern Nepal, Sikkim, western Bhutan and southwestern China (Xizang), growing at 3000–4100 m altitude. It is a medium- sized deciduous coniferous tree reaching 20–25 m tall, with a trunk up to 0.8 m diameter. The crown is slender conic; the main branches are level to upswept, the side branchlets pendulous from them. The shoots are dimorphic, with growth divided into long shoots (typically 10–50 cm long) and bearing several buds, and short shoots only 1–2 mm long with only a single bud.
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It is said in the preface that Newton revised and corrected these lectures, adding matter of his own, but it seems probable from Newton's remarks in the fluxional controversy that the additions were confined to the parts which dealt with optics. This, which is his most important work in mathematics, was republished with a few minor alterations in 1674. In 1675 he published an edition with numerous comments of the first four books of the On Conic Sections of Apollonius of Perga, and of the extant works of Archimedes and Theodosius of Bithynia. In the optical lectures many problems connected with the reflection and refraction of light are treated with ingenuity.
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It is a medium-sized to large deciduous coniferous tree reaching 20–40 m tall, with a trunk up to 1 m diameter. The crown is broad conic; both the main branches and the side branches are level, the side branches only rarely drooping. The shoots are dimorphic, with growth divided into long shoots (typically 10–50 cm long) and bearing several buds, and short shoots only 1–2 mm long with only a single bud. The leaves are needle-like, light glaucous green, 2–5 cm long; they turn bright yellow to orange before they fall in the autumn, leaving the pinkish-brown shoots bare until the next spring.
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The church has an octagonal dome covered with a conic floor and once housed a masterfully ornate stone iconostasis which is now on display at the Art Museum of Georgia in Tbilisi. The monastery was somewhat altered in the 11th and 18th centuries, but has largely retained its original architecture. The Upper Church (zemo eklesia) named after the Theotokos is a central part of the Shio-Mgvime complex constructed at the verge of the 12th century at the behest of King David IV of Georgia. Initially a domed church, it was subsequently destroyed by a foreign invasion and restored, in 1678, as a basilica.
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3a, the optical elements are oriented so that S'1 and S'2 are in line with the observer, and the resulting interference pattern consists of circles centered on the normal to M1 and M'2 (fringes of equal inclination). If, as in Fig. 3b, M1 and M'2 are tilted with respect to each other, the interference fringes will generally take the shape of conic sections (hyperbolas), but if M1 and M'2 overlap, the fringes near the axis will be straight, parallel, and equally spaced (fringes of equal thickness). If S is an extended source rather than a point source as illustrated, the fringes of Fig.
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The first three books of this treatise were translated into English and, several times, printed as The Elements of the Conic Sections. In 1749, was published Apollonii Pergaei locorum planorum libri II., a restoration of Apollonius's lost treatise, founded on the lemmas given in the seventh book of Pappus's Mathematical Collection. In 1756, appeared, both in Latin and in English, the first edition of his Euclid's Elements. This work, which contained only the first six and the eleventh and twelfth books, and to which, in its English version, he added the Data in 1762, was for long the standard text of Euclid in England.
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Also, many mathematical theories, which had seemed to be totally pure mathematics, were eventually used in applied areas, mainly physics and computer science. A famous early example is Isaac Newton's demonstration that his law of universal gravitation implied that planets move in orbits that are conic sections, geometrical curves that had been studied in antiquity by Apollonius. Another example is the problem of factoring large integers, which is the basis of the RSA cryptosystem, widely used to secure internet communications. It follows that, presently, the distinction between pure and applied mathematics is more a philosophical point of view or a mathematician's preference than a rigid subdivision of mathematics.
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As the tree ages, much of its vascular cambium layer may die. In very old specimens, often only a narrow strip of living tissue connects the roots to a handful of live branches. The Great Basin bristlecone pine differs from the Rocky Mountain bristlecone pine in that the needles of the former always have two uninterrupted resin canals, so it lacks the characteristic small white resin flecks appearing on the needles of the latter. The Great Basin bristlecone pine differs from the foxtail pine because the cone bristles of the former are over long, and the cones have a more rounded (not conic) base.
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Projective spaces are widely used in geometry, as allowing simpler statements and simpler proofs. For example, in affine geometry, two distinct lines in a plane intersect in at most one point, while, in projective geometry, they intersect in exactly one point. Also, there is only one class of conic sections, which can be distinguished only by their intersections with the line at infinity: two intersection points for hyperbolas; one for the parabola, which is tangent to the line at infinity; and no real intersection point of ellipses. In topology, and more specifically in manifold theory, projective spaces play a fundamental role, being typical examples of non-orientable manifolds.
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The complex line at infinity was much used in nineteenth century geometry. In fact one of the most applied tricks was to regard a circle as a conic constrained to pass through two points at infinity, the solutions of :X2 \+ Y2 = 0. This equation is the form taken by that of any circle when we drop terms of lower order in X and Y. More formally, we should use homogeneous coordinates :[X:Y:Z] and note that the line at infinity is specified by setting : Z = 0. Making equations homogeneous by introducing powers of Z, and then setting Z = 0, does precisely eliminate terms of lower order.
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The two diagonals and the two tangency chords are concurrent.Yiu, Paul, Euclidean Geometry, , 1998, pp. 156–157.Grinberg, Darij, Circumscribed quadrilaterals revisited, 2008 One way to see this is as a limiting case of Brianchon's theorem, which states that a hexagon all of whose sides are tangent to a single conic section has three diagonals that meet at a point. From a tangential quadrilateral, one can form a hexagon with two 180° angles, by placing two new vertices at two opposite points of tangency; all six of the sides of this hexagon lie on lines tangent to the inscribed circle, so its diagonals meet at a point.
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A number of Geological Conservation Review sites have been identified within the national park, about half of which have been designated as sites of special scientific interest (SSSIs). The Falls of Dochart, the delta of the River Balvag (Loch Lubnaig Marshes) and the River Endrick have all been notified as SSSIs for their fluvial geomorphology whilst mass movement sites at Ben Vane, Glen Ample and Beinn Arthur (The Cobbler) have been declared GCR sites but not notified as SSSIs. Other Quaternary sites include Croftamie, Portnellan-Ross Priory-Claddochside and the Menteith moraine which is partly within Flanders Moss SSSI. Igneous GCRs include Balmaha & Arrochymore Point (as Conic Hill SSSI) and Garabal Hill.
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Cupressus bakeri−Hesperocyparis bakeri is an evergreen tree with a conic crown, growing to heights of (exceptionally to 39 meters−130 feet), and a trunk diameter of up to 50 cm (20 inches) (exceptionally to 1 meter—40 inches). The foliage grows in sparse, very fragrant, usually pendulous sprays, varying from dull gray-green to glaucous blue-green in color. The leaves are scale-like, 2–5 mm long, and produced on rounded (not flattened) shoots.Pinetum Photos, trees The seed cones are globose to oblong, covered in warty resin glands, 10–25 mm long, with 6 or 8 (rarely 4 or 10) scales, green to brown at first, maturing gray or gray-brown about 20–24 months after pollination.
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The study of these two hyperboloids is, therefore, in this way connected very simply, through biquaternions, with the study of the sphere; ... In this passage is the operator giving the scalar part of a quaternion, and is the "tensor", now called norm, of a quaternion. A modern view of the unification of the sphere and hyperboloid uses the idea of a conic section as a slice of a quadratic form. Instead of a conical surface, one requires conical hypersurfaces in four-dimensional space with points determined by quadratic forms. First consider the conical hypersurface :P = \lbrace p \ : \ w^2 = x^2 + y^2 + z^2 \rbrace and :H_r = \lbrace p \ :\ w = r \rbrace , which is a hyperplane.
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Hence, any distance whose ratio to an existing distance is the solution of a cubic or a quartic equation is constructible. Using a markable ruler, regular polygons with solid constructions, like the heptagon, are constructible; and John H. Conway and Richard K. Guy give constructions for several of them.Conway, John H. and Richard Guy: The Book of Numbers The neusis construction is more powerful than a conic drawing tool, as one can construct complex numbers that do not have solid constructions. In fact, using this tool one can solve some quintics that are not solvable using radicals.A. Baragar, "Constructions using a Twice-Notched Straightedge", The American Mathematical Monthly, 109 (2), 151 -- 164 (2002).
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It is essentially the first experimental and exploratory phase of an art movement that would become altogether more extreme, known from the spring of 1911 as Cubism. Proto-Cubist artworks typically depict objects in geometric schemas of cubic or conic shapes. The illusion of classical perspective is progressively stripped away from objective representation to reveal the constructive essence of the physical world (not just as seen). The term is applied not only to works of this period by Georges Braque and Pablo Picasso, but to a range of art produced in France during the early 1900s, by such artists as Jean Metzinger, Albert Gleizes, Henri Le Fauconnier, Robert Delaunay, Fernand Léger, and to variants developed elsewhere in Europe.
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Larix gmelinii is a medium-sized deciduous coniferous tree reaching 10–30 m tall, rarely 40 m, with a trunk up to 1 m diameter. The crown is broad conic; both the main branches and the side branches are level, the side branches only rarely drooping. The shoots are dimorphic, with growth divided into long shoots (typically 5–30 cm long) and bearing several buds, and short shoots only 1–2 mm long with only a single bud. The leaves are needle-like, light green, 2–3 cm long; they turn bright yellow to orange before they fall in the autumn, leaving the variably downy reddish-brown shoots bare until the next spring.
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Old advertising display of items used in cotton textile manufacture during the industrial revolution Rev John Dyer of Northampton recognised the importance of the Paul and Wyatt cotton spinning machine in a poem in 1757: > A circular machine, of new design > In conic shape: it draws and spins a thread > Without the tedious toil of needless hands. > A wheel invisible, beneath the floor, > To ev'ry member of th' harmonius frame, > Gives necessary motion. One intent > O'erlooks the work; the carded wool, he says, > So smoothly lapped around those cylinders, > Which gently turning, yield it to yon cirue > Of upright spindles, which with rapid whirl > Spin out in long extenet an even twine.
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