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"parallelogram" Definitions
  1. a flat shape with four straight sides, the opposite sides being the same distance apart at every point and equal to each otherTopics Colours and Shapesc2

442 Sentences With "parallelogram"

How to use parallelogram in a sentence? Find typical usage patterns (collocations)/phrases/context for "parallelogram" and check conjugation/comparative form for "parallelogram". Mastering all the usages of "parallelogram" from sentence examples published by news publications.

The black parallelogram (whose bottom edge reflects that of the gray parallelogram) contrasts strongly with the gray parallelogram, yet connects color-wise to the bold yellow at the bottom.
What space does the gray parallelogram in the middle occupy?
This is contradicted by the horizontal top edge of the gray parallelogram.
The yellow trapezoid suggests a receding plane, while the bottom diagonal edge of the gray parallelogram echoes that illusion.
Just to the right of the green brushstroke Shear has made a blue parallelogram out of a few overlapping strokes.
Think about it: a square or rectangle can easily be pressured into a parallelogram without changing the length of its sides.
We can rotate any triangle 19683 degrees about the midpoint of one of its sides to make a parallelogram, which tiles easily.
Above these two canvases is a large black parallelogram whose right and left edges align with the base of the yellow trapezoid.
The company plans to replace the familiar checkmark badge with a muted gray parallelogram banner whose meaning could not be less clear.
Two halves of a curving black parallelogram, one half partially occluded by the seagrass and drifting yellow circles, sweep from side to side.
He later came up with the concept of an undulating pier floating on a forest of piles in the shape of a parallelogram.
That's the bug of irritation that sets Bruce Norris's "A Parallelogram" swatting for more than two hours at a target it can't hit.
"A Parallelogram" is filled with them, but as they are all variations on the same fatalistic theme, they offer diminishing returns of pleasure.
And its wide-ranging keystone corrections mean you can project a perfect parallelogram even when placed at extreme angles from the wall or screen.
Three feet high, it is a series of discrete rhomboids — imagine a cube stretched at opposing corners, so that every side is a parallelogram.
Mr. Diller eventually suggested that Pier 54 be replaced with an entirely new, 2.4-acre pier shaped like a parallelogram, with three performance venues amid trees.
Directly above it is a gray parallelogram, whose right and left edges are aligned with the top left and right edge of the yellow trapezoid below.
"A Parallelogram" had its premiere in 2010, the same year as Mr. Norris's Pulitzer- and Tony-winning "Clybourne Park," but it's only now arriving in New York.
With the Scorpion, Juiced is abandoning the parallelogram shape of the Scrambler for a step-through frame that's probably more approachable to a wider range of people.
I can still unfurl it and get a parallelogram which has the same area as the rectangle (= base x height), so the surface area stays the same, right?
The parallelogram of the title, therefore, isn't the shape you remember from geometry; it's more of a pun, suggesting a message, like a telegram, from a parallel reality.
Instead it's a parallelogram, with a trigger on an inside corner and a big glowing bulb (so your Playstation Camera can track its movements) on the opposite outside corner.
Designed by the architect Stuart Narofsky, the eight-story parallelogram-shaped structure fashioned from glass, timber and native Comanche stone is located in Calacoto, an upscale neighborhood in La Paz.
My first attempts were not very good because I did not use a frame and because I tugged the threads too tightly, the piece turned from a square to a parallelogram.
She tried to force the image she'd glimpsed briefly in BargeView, the whole structure a neatly delineated parallelogram, but another shape summoned itself: a long, cylindrical sheath for a heavy ceremonial dagger.
Coupled with the transition away from a highly recognizable checkmark symbol to a muted gray parallelogram flag gizmo, YouTube has handled a hugely consequential decision in one of the strangest ways imaginable.
His greatest mark on Boston is the Hancock building, an 800-foot-tall glass parallelogram that towers over Trinity Church, a beloved Romanesque edifice by the 933th-century architect Henry Hobson Richardson.
"My instinct is to try to point toward things in society that are stupid and to laugh," he said in an interview for the premiere of "A Parallelogram" at the Steppenwolf Theater Company in Chicago.
In Bruce Norris's time-shifting play "A Parallelogram," Bee sees and hears someone Jay can't: a decades-older version of herself who's puffing away, chatting with her about the futility of trying to alter the future.
In fact, she does the opposite: "Foolish," a small head on the floor by the gallery's entrance, has a large parallelogram cut out of its protruding top, revealing the empty space inside and traces of paper scraps and glue.
Bradford's abilities with a single, unaltered, calligraphic line are most evident in the three figures at the far end of the tilted table's outlined plane (which forms a parallelogram), the tops of their heads sitting just below the painting's top edge.
In some, there are circuit boards, as in "Tightrope: Narcissism" (2017), where they form a dark parallelogram in a field of red; it's a city floating in an architectural diagram, or a tear in the patina that reveals what's underneath.
Diller Scofidio + Renfro and the Rockwell Group, the architects, have given it a deliberately makeshift look: its dominant feature is a puffy-surfaced, parallelogram-shaped shell, which rests on giant wheels and can be rolled out to enclose part of the main plaza.
The midpoint polygon of a quadrilateral is a parallelogram called its Varignon parallelogram. If the quadrilateral is simple, the area of the parallelogram is one half the area of the original quadrilateral. The perimeter of the parallelogram equals the sum of the diagonals of the original quadrilateral.
It can be seen from the diagram that x = 0 for a parallelogram, and so the general formula simplifies to the parallelogram law.
A parallelogram. The sides are shown in blue and the diagonals in red. In mathematics, the simplest form of the parallelogram law (also called the parallelogram identity) belongs to elementary geometry. It states that the sum of the squares of the lengths of the four sides of a parallelogram equals the sum of the squares of the lengths of the two diagonals.
The midpoints of the sides of an arbitrary quadrilateral are the vertices of a parallelogram, called its Varignon parallelogram. If the quadrilateral is convex or concave (that is, not self-intersecting), then the area of the Varignon parallelogram is half the area of the quadrilateral.
If the triangle is moved to the other side of the trapezoid, then the resulting figure is a rectangle. It follows that the area of the parallelogram is the same as the area of the rectangle: : (parallelogram). A parallelogram split into two equal triangles. However, the same parallelogram can also be cut along a diagonal into two congruent triangles, as shown in the figure to the right.
The Varignon parallelogram is a rhombus if and only if the two diagonals of the quadrilateral have equal length, that is, if the quadrilateral is an equidiagonal quadrilateral.. The Varignon parallelogram is a rectangle if and only if the diagonals of the quadrilateral are perpendicular, that is, if the quadrilateral is an orthodiagonal quadrilateral. If a crossing quadrilateral is formed from either pair of opposite parallel sides and the diagonals of a parallelogram, the Varignon parallelogram is a line segment traversed twice.
The mathematical proof of the parallelogram of force is not generally accepted to be mathematically valid. Various proofs were developed (chiefly Duchayla's and Poisson's), and these also caused objections. That the parallelogram of force was true was not questioned, but why it was true. Today the parallelogram of force is accepted as an empirical fact, non-reducible to Newton's first principles.
Steiner generation can also be defined for hyperbolas and parabolas. It is sometimes called a parallelogram method because one can use other points rather than the vertices, which starts with a parallelogram instead of a rectangle.
Fundamental parallelogram defined by a pair of vectors in the complex plane.
77–78 () The lower figure shows the elements of the proof. Focus on the left side of the figure. The left green parallelogram has the same area as the left, blue portion of the bottom parallelogram because both have the same base b and height h. However, the left green parallelogram also has the same area as the left green parallelogram of the upper figure, because they have the same base (the upper left side of the triangle) and the same height normal to that side of the triangle.
These shapes are rhomboids Traditionally, in two-dimensional geometry, a rhomboid is a parallelogram in which adjacent sides are of unequal lengths and angles are non-right angled. A parallelogram with sides of equal length (equilateral) is a rhombus but not a rhomboid. A parallelogram with right angled corners is a rectangle but not a rhomboid. The term rhomboid is now more often used for a rhombohedron or a more general parallelepiped, a solid figure with six faces in which each face is a parallelogram and pairs of opposite faces lie in parallel planes.
Remark: # The Steiner generation exists for ellipses and parabolas, too. # The Steiner generation is sometimes called a parallelogram method because one can use other points rather than the vertices, which starts with a parallelogram instead of a rectangle.
A convex quadrilateral is equidiagonal if and only if its Varignon parallelogram, the parallelogram formed by the midpoints of its sides, is a rhombus. An equivalent condition is that the bimedians of the quadrilateral (the diagonals of the Varignon parallelogram) are perpendicular. A convex quadrilateral with diagonal lengths p and q and bimedian lengths m and n is equidiagonal if and only if :pq=m^2+n^2.
A parallelogram is a trapezoid with two pairs of parallel sides. A parallelogram has central 2-fold rotational symmetry (or point reflection symmetry). It is possible for obtuse trapezoids or right trapezoids (rectangles). A tangential trapezoid is a trapezoid that has an incircle.
The same technique applies for the X load (25 watts) rating except inside a 0.6% accuracy parallelogram.
It follows from the correspondence between zonohedra and arrangements, and from the Sylvester–Gallai theorem which (in its projective dual form) proves the existence of crossings of only two lines in any arrangement, that every zonohedron has at least one pair of opposite parallelogram faces. (Squares, rectangles, and rhombuses count for this purpose as special cases of parallelograms.) More strongly, every zonohedron has at least six parallelogram faces, and every zonohedron has a number of parallelogram faces that is linear in its number of generators.
A rectangle is a special case of both parallelogram and trapezoid. A square is a special case of a rectangle.
The building had the shape of a parallelogram. When seen from the air, the building resembled a Star of David.
Parallelogram ABCD To prove that the diagonals of a parallelogram bisect each other, we will use congruent triangles: :\angle ABE \cong \angle CDE (alternate interior angles are equal in measure) :\angle BAE \cong \angle DCE (alternate interior angles are equal in measure). (since these are angles that a transversal makes with parallel lines AB and DC). Also, side AB is equal in length to side DC, since opposite sides of a parallelogram are equal in length. Therefore, triangles ABE and CDE are congruent (ASA postulate, two corresponding angles and the included side).
For an ellipse, two diameters are said to be conjugate if and only if the tangent line to the ellipse at an endpoint of one diameter is parallel to the other diameter. Each pair of conjugate diameters of an ellipse has a corresponding tangent parallelogram, sometimes called a bounding parallelogram, formed by the tangent lines to the ellipse at the four endpoints of the conjugate diameters. All tangent parallelograms for a given ellipse have the same area. It is possible to reconstruct an ellipse from any pair of conjugate diameters, or from any tangent parallelogram.
Charles Jeantaud Jeantaud Milord, 1898 Charles Jeantaud (1840-1906) was a French engineer who invented the parallelogram steering linkage in 1878.
A shearing force is applied to the top of the rectangle while the bottom is held in place. The resulting shear stress, , deforms the rectangle into a parallelogram. The area involved would be the top of the parallelogram. 'Shear stress, often denoted by ' (Greek: tau), is the component of stress coplanar with a material cross section.
The house features parallelograms; indeed, the only right angles to be found in the house are located in the bathroom. Even the bed is a parallelogram and sheets must be custom made. The house itself sits on a parallelogram blueprint. The house features a carport, attached shed, and a workroom for Kraus, a glass work artist.
Copper(II) fluoride has a monoclinic crystal structure and cannot achieve a higher-symmetry structure. It forms rectangular prisms with a parallelogram base.
In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. The congruence of opposite sides and opposite angles is a direct consequence of the Euclidean parallel postulate and neither condition can be proven without appealing to the Euclidean parallel postulate or one of its equivalent formulations. By comparison, a quadrilateral with just one pair of parallel sides is a trapezoid in American English or a trapezium in British English.
The three-dimensional counterpart of a parallelogram is a parallelepiped. The etymology (in Greek παραλληλ- όγραμμον, a shape "of parallel lines") reflects the definition.
Repeating the argument for the right side of the figure, the bottom parallelogram has the same area as the sum of the two green parallelograms.
Every convex polygon with area T can be inscribed in a triangle of area at most equal to 2T. Equality holds (exclusively) for a parallelogram.
Heath (1981) pp. 78-79 Later, the term was used for an L-shaped instrument like a steel square used to draw right angles. This shape may explain its use to describe a shape formed by cutting a smaller square from a larger one. Euclid extended the term to the plane figure formed by removing a similar parallelogram from a corner of a larger parallelogram.
A second pair of parallelogram links maintains vertical correspondence between the two pens ("D" and "E" on diagram). These consist of two variable parallelogram frames attached at a common edge, one of which is also attached to the bridge, while the other is attached to one of the pen supports at each corner. The projecting sides of the upper frame consist of parallel linkages.
The base pairs form a parallelogram with half the area of the quadrilateral, Aq, as the sum of the areas of the four large triangles, Al is 2 Aq (each of the two pairs reconstructs the quadrilateral) while that of the small triangles, As is a quarter of Al (half linear dimensions yields quarter area), and the area of the parallelogram is Aq minus As.
Sander illusion The Sander illusion or Sander's parallelogram is an optical illusion described by the German psychologist Friedrich Sander (1889–1971) in 1926. However, it had been published earlier by Matthew Luckiesh in his 1922 book Visual Illusions: Their Causes, Characteristics, and Applications. The diagonal line bisecting the larger, left-hand parallelogram appears to be considerably longer than the diagonal line bisecting the smaller, right-hand parallelogram, but is the same length. One possible reason for this illusion is that the diagonal lines around the blue lines give a perception of depth, and when the blue lines are included in that depth, they are perceived as different lengths.
History of the Tour de France: 1920–1939 - Les Forcats de la Route by Mitch Mueller Derailleurs did not become common road racing equipment until 1938 when Simplex introduced a cable-shifted derailleur. In 1949 Campagnolo introduced the Gran Sport, a more refined version of the then already existing, yet less commercially successful, cable-operated parallelogram rear derailleurs. In 1964, Suntour invented the slant-parallelogram rear derailleur, which let the jockey pulley maintain a more constant distance from the different sized sprockets, resulting in easier shifting. Once the patents expired, other manufacturers adopted this design, at least for their better models, and the "slant parallelogram" remains the current rear derailleur pattern.
If it is desired to remain within real numbers, there are two cases to consider: and . The period parallelogram is either a square or a rhombus.
A Roberval balance. The pivots of the parallelogram understructure makes it insensitive to load positioning away from center, so improves its accuracy, and ease of use.
The same position vector x represented in two 3d rectangular coordinate systems each with an orthonormal basis, the cuboids illustrate the parallelogram law for adding vector components.
The following examples show that a bivector in two dimensions measures the area of a parallelogram, and the magnitude of a bivector in three dimensions also measures the area of a parallelogram. Similarly, a three-vector in three dimensions measures the volume of a parallelepiped. It is easy to check that the magnitude of a three-vector in four dimensions measures the volume of the parallelepiped spanned by these vectors.
Principle of the linear planimeter The working of the linear planimeter may be explained by measuring the area of a rectangle ABCD (see image). Moving with the pointer from A to B the arm EM moves through the yellow parallelogram, with area equal to PQ×EM. This area is also equal to the area of the parallelogram A"ABB". The measuring wheel measures the distance PQ (perpendicular to EM).
Most other simple formulas for area follow from the method of dissection. This involves cutting a shape into pieces, whose areas must sum to the area of the original shape. A diagram showing how a parallelogram can be re-arranged into the shape of a rectangle. For an example, any parallelogram can be subdivided into a trapezoid and a right triangle, as shown in figure to the left.
The area K of an equidiagonal quadrilateral can easily be calculated if the length of the bimedians m and n are known. A quadrilateral is equidiagonal if and only if. . :\displaystyle K=mn. This is a direct consequence of the fact that the area of a convex quadrilateral is twice the area of its Varignon parallelogram and that the diagonals in this parallelogram are the bimedians of the quadrilateral.
Right-handed parallelogram machine with a ballast. A drafting machine is a device which is mounted to the drawing board. It has rulers whose angles can be precisely adjusted with a controlling mechanism. There are two main types of apparatus: an arm-type parallelogram apparatus based on a hinged arm; and a track-type apparatus which moves on a rail mounted to the top of the drawing board.
Using gyrotrigonometry, a gyrovector addition can be found which operates according to the gyroparallelogram law. This is the coaddition to the gyrogroup operation. Gyroparallelogram addition is commutative. The gyroparallelogram law is similar to the parallelogram law in that a gyroparallelogram is a hyperbolic quadrilateral the two gyrodiagonals of which intersect at their gyromidpoints, just as a parallelogram is a Euclidean quadrilateral the two diagonals of which intersect at their midpoints.
The midpoints of the sides of an arbitrary quadrilateral form a parallelogram. If the quadrilateral is convex or concave (not complex), then the area of the parallelogram is half the area of the quadrilateral. If one introduces the concept of oriented areas for n-gons, then this area equality also holds for complex quadrilaterals.Coxeter, H. S. M. and Greitzer, S. L. "Quadrangle; Varignon's theorem" §3.1 in Geometry Revisited.
Rectangles in this shape are rep-2. A rectangle (or parallelogram) is rep-n if its aspect ratio is :1. An isosceles right triangle is also rep-2.
Washington, DC: Math. Assoc. Amer., pp. 52-54, 1967. The Varignon parallelogram exists even for a skew quadrilateral, and is planar whether the quadrilateral is planar or not.
Generalization for arbitrary triangles, green area Construction for proof of parallelogram generalization Pappus's area theorem is a further generalization, that applies to triangles that are not right triangles, using parallelograms on the three sides in place of squares (squares are a special case, of course). The upper figure shows that for a scalene triangle, the area of the parallelogram on the longest side is the sum of the areas of the parallelograms on the other two sides, provided the parallelogram on the long side is constructed as indicated (the dimensions labeled with arrows are the same, and determine the sides of the bottom parallelogram). This replacement of squares with parallelograms bears a clear resemblance to the original Pythagoras's theorem, and was considered a generalization by Pappus of Alexandria in 4 ADFor the details of such a construction, see Claudi Alsina, Roger B. Nelsen: Charming Proofs: A Journey Into Elegant Mathematics. MAA, 2010, , pp.
Any line through the midpoint of a parallelogram bisects the areaDunn, J. A., and J. E. Pretty, "Halving a triangle", Mathematical Gazette 56, May 1972, p. 105. and the perimeter.
Thus, L2(R) is also a complete seminormed vector space satisfying the parallelogram identity. But we actually get a bit more, since the space is now T0. A seminorm is a norm if and only if the underlying topology is T0, so L2(R) is actually a complete normed vector space satisfying the parallelogram identity--otherwise known as a Hilbert space. And it is a Hilbert space that mathematicians (and physicists, in quantum mechanics) generally want to study.
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.
The familiar notion of vector addition for velocities in the Euclidean plane can be done in a triangular formation, or since vector addition is commutative, the vectors in both orderings geometrically form a parallelogram (see "parallelogram law"). This does not hold for relativistic velocity addition; instead a hyperbolic triangle arises whose edges are related to the rapidities of the boosts. Changing the order of the boost velocities, one does not find the resultant boost velocities to coincide.
By changing the positions of the arms in the linkage between the pointer arm and drawing arm, the scale of the image produced can be changed. Diagram illustrating the principles used by William Wallace's eidograph In 1821, Professor William Wallace (1768–1843) invented the eidograph to improve upon the practical utility of the pantograph. The eidograph relocates the fixed point to the center of the parallelogram and uses a narrow parallelogram to provide improved mechanical advantages.
The fundamental parallelogram contains no further lattice points in its interior or boundary. Conversely, any pair of lattice points with this property constitute a fundamental pair, and furthermore, they generate the same lattice.
Traynor YBA-3 Custom Special Amp showing the 1970 parallelogram nameplate In 1970, Traynor introduced the new Traynor logo (in the shape of a parallelogram) that was less prone to having the initial 'T' and final 'r' break off to become "rayno". In 1976, Peter Traynor left Yorkville Sound, suffering from a bad back. The Traynor brand would be slowly phased out over the next 17 years until its reintroduction in 2000. In 2011, Traynor products are manufactured in Pickering, Ontario.
Such experiments demonstrate the crucial properties that forces are additive vector quantities: they have magnitude and direction. When two forces act on a point particle, the resulting force, the resultant (also called the net force), can be determined by following the parallelogram rule of vector addition: the addition of two vectors represented by sides of a parallelogram, gives an equivalent resultant vector that is equal in magnitude and direction to the transversal of the parallelogram. The magnitude of the resultant varies from the difference of the magnitudes of the two forces to their sum, depending on the angle between their lines of action. However, if the forces are acting on an extended body, their respective lines of application must also be specified in order to account for their effects on the motion of the body.
It may also be drawn by a mechanical linkage in the form of Watt's linkage, with the lengths of the three bars of the linkage and the distance between its endpoints chosen to form a crossed parallelogram..
Thales's theorem and reflections Let ABC be a triangle in a circle where AB is a diameter in that circle. Then construct a new triangle ABD by mirroring triangle ABC over the line AB and then mirroring it again over the line perpendicular to AB which goes through the center of the circle. Since lines AC and BD are parallel, likewise for AD and CB, the quadrilateral ACBD is a parallelogram. Since lines AB and CD are both diameters of the circle and therefore are equal length, the parallelogram must be a rectangle.
The parallelogram of forces is a method for solving (or visualizing) the results of applying two forces to an object. Figure 1: Parallelogram construction for adding vectors When more than two forces are involved, the geometry is no longer parallelogrammatic, but the same principles apply. Forces, being vectors are observed to obey the laws of vector addition, and so the overall (resultant) force due to the application of a number of forces can be found geometrically by drawing vector arrows for each force. For example, see Figure 1.
The steps of this theorem require nothing beyond basic constructive Euclidean geometry. With the additional construction of a parallelogram having sides parallel to the diagonals, and tangent to the corners of the rectangle of incenters, the quadrilateral case of the cyclic polygon theorem can be proved in a few steps. The equality of the sums of the radii of the two pairs is equivalent to the condition that the constructed parallelogram be a rhombus, and this is easily shown in the construction. Another proof of the quadrilateral case is available due to Wilfred Reyes (2002).
The elongated dodecahedron, a zonohedron. Its eight red parallelogram faces correspond to ordinary points of a five-line arrangement; an equivalent form of the Sylvester–Gallai theorem states that every zonohedron has at least one parallelogram face. Arrangements of lines have a combinatorial structure closely connected to zonohedra, polyhedra formed as the Minkowski sum of a finite set of line segments, called generators. In this connection, each pair of opposite faces of a zonohedron corresponds to a crossing point of an arrangement of lines in the projective plane, with one line for each generator.
The 304 was the second and last glider developed by Glasflügel in cooperation with Schempp-Hirth. It superseded the Glasflügel Mosquito. The principal designer of the 304 was Martin Hansen, known for his role in the design of the Akaflieg Braunschweig SB-11. The glider continued the Glasflügel tradition of innovation: the parallelogram control stick, combined trailing edge flaps and airbrakes, automatic trimming, heel-operated brakes, automatic control connections, the extremely easy assembly of the wings and tailplane, the parallelogram forward-opening canopy and lifting instrument panel are Glasflügel innovations largely copied by other manufacturers.
For squares on two sides of an arbitrary triangle it yields a parallelogram of equal area over the third side and if the two sides are the legs of a right angle the parallelogram over the third side will be square as well. For a right-angled triangle, two parallelograms attached to the legs of the right angle yield a rectangle of equal area on the third side and again if the two parallelograms are squares then the rectangle on the third side will be a square as well.
The method starts by assuming that objects undergo globally rigid transformations. Because smooth surfaces are locally planar, affine invariant features are appropriate for matching: the paper detects ellipse-shaped regions of interest using both edge-like and blob-like features, and as per [Lowe 2004], finds the dominant gradient direction of the ellipse, converts the ellipse into a parallelogram, and takes a SIFT descriptor on the resulting parallelogram. Color information is used also to improve discrimination over SIFT features alone. Partial models of features, projected into 3D, constructed from nearby views of a teddy-bear.
Levi-Civita's parallelogramoid In the mathematical field of differential geometry, the Levi-Civita parallelogramoid is a quadrilateral in a curved space whose construction generalizes that of a parallelogram in the Euclidean plane. It is named for its discoverer, Tullio Levi-Civita. Like a parallelogram, two opposite sides AA′ and BB′ of a parallelogramoid are parallel (via parallel transport side AB) and the same length as each other, but the fourth side A′B′ will not in general be parallel to or the same length as the side AB, although it will be straight (a geodesic).
In Euclidean plane geometry terms, being a parallelogram is affine since affine transformations always take one parallelogram to another one. Being a circle is not affine since an affine shear will take a circle into an ellipse. To explain accurately the relationship between affine and Euclidean geometry, we now need to pin down the group of Euclidean geometry within the affine group. The Euclidean group is in fact (using the previous description of the affine group) the semi- direct product of the orthogonal (rotation and reflection) group with the translations.
Aluminum signs: on white background a yellow rhombus with black outline, with the words E4/6 in black. Coloured signs on rocks and trees: white background, a yellow parallelogram on the left and a black on the right.
Both cars shared clean, slab-sided body panels, thick C-pillars, and a chrome molding outlining the top of the fender line. However, Engel used subtle curves and parallelogram angles to give the Imperial a distinct and novel look.
Without bracing an antiparallelogram linkage can be turned into a normal parallelogram. It can be braced to stop this happening using a construction by Abbott and Barton 2004. This construction can be used to fix a problem in Kempe's Universality Theorem.
The square is one such quadrilateral, but there are infinitely many others. An orthodiagonal quadrilateral that is also equidiagonal is a midsquare quadrilateral because its Varignon parallelogram is a square. Its area can be expressed purely in terms of its sides.
Using the visualization of complex numbers in the complex plane, the addition has the following geometric interpretation: the sum of two complex numbers a and b, interpreted as points in the complex plane, is the point obtained by building a parallelogram from the three vertices O, and the points of the arrows labeled a and b (provided that they are not on a line). Equivalently, calling these points A,\; B, respectively and the fourth point of the parallelogram X, the triangles OAB and XBA are congruent. A visualization of the subtraction can be achieved by considering addition of the negative subtrahend.
K & E LEROY lettering set (1959) Mechanical lettering is sometimes done using a pantograph, a device consisting of four bars ("links") which are pinned to each other to form a parallelogram. The links can pivot about these pins. The lowermost link of the parallelogram is fixed to two rigid supports. One vertical link at one end is connected to a profile tracer, which traces the profile of the letter to be drawn, and the second vertical link and the other horizontal link are jointly connected to a pencil that draws the exact shape of the profile traced.
In one direction, the creases lie along straight lines, with each parallelogram forming the mirror reflection of its neighbor across each crease. In the other direction, the creases zigzag, and each parallelogram is the translation of its neighbor across the crease. Each of the zigzag paths of creases consists solely of mountain folds or of valley folds, with mountains alternating with valleys from one zigzag path to the next. Each of the straight paths of creases alternates between mountain and valley folds.. Reproduced in British Origami, 1981, and online at the British Origami Society web site.
In October 1862, the Commissioners' architect checking on the building declared it unsafe. The roof was too heavy and the walls had bowed out. It was described as a very plain, unpretending structure, an undivided parallelogram, 72 ft long, and 55 ft wide.
The parallelogram rule used for the addition of forces, however, dates from antiquity and is noted explicitly by Galileo and Newton.Michael J. Crowe (1967). A History of Vector Analysis : The Evolution of the Idea of a Vectorial System. Dover Publications (reprint edition; ).
A trapezium as any quadrilateral more general than a parallelogram is the sense of the term in Euclid. Confusingly, the word trapezium was sometimes used in England from c. 1800 to c. 1875, to denote an irregular quadrilateral having no sides parallel.
Scenic Jungle in Division Sahiwal Sahiwal Division is in the southeast of Punjab. From Multan Division it lies between 30-40 north latitude and 73-06 longitude. It is above sea level. It forms a parallelogram lying NE-SW along the River Ravi.
Propalene or bicyclo[1.1.0]buta-1,3-diene is a polycyclic hydrocarbon composed of two fused cyclopropene rings. Computational studies indicate that the molecule is planar, with the carbon framework forming a parallelogram that has distinctly alternating short and long carbon–carbon bonds.
If no change occurs and there is no effect, then there is no force. Force, gravity, and attraction are mathematical, hypothetical abstractions and they are not found in nature as physical qualities. The parallelogram of composite forces is not a physical quality. It is mathematical.
Other hyperbolic invariants include the shape of the fundamental parallelogram, length of shortest geodesic, and volume. Modern knot and link tabulation efforts have utilized these invariants effectively. Fast computers and clever methods of obtaining these invariants make calculating these invariants, in practice, a simple task .
The fort was built on a hill, 60 yards west of the Allegheny River. The fort was in the form of a parallelogram, about 75 by . The curtain was made of hewed timber, stacked lengthwise. The four corners had bastions in the form of polygons.
If the incident beam is linearly polarized at some other inclination, the emerging beam is elliptically polarized with one principal axis in the plane of reflection, and vice versa. The rhomb usually takes the form of a right parallelepiped — that is, a right parallelogram- based prism. If the incident ray is perpendicular to one of the smaller rectangular faces, the angle of incidence and reflection at the next face is equal to the acute angle of the parallelogram. This angle is chosen so that each reflection introduces a phase difference of 45° between the components polarized parallel and perpendicular to the plane of reflection.
Hurling goalkeeper In hurling, the goalkeeper's main task is to prevent a goal from being scored against his side by directly defending the team's goal. He also takes "puckouts" after a score or wide ball. A goal occurs when the ball passes through the goal; the attacking team is awarded 3 points. The goalkeeper has one special rule pertaining to him, opposing players may not directly physically challenge him while he is in possession of the ball in the small parallelogram, although they may harass him, while if he leaves the small parallelogram he is subject to the same rules as all other players.
A cyclic voltammogram shows the fundamental difference of the current curves between static capacitors and pseudocapacitors Pseudocapacitance properties can be expressed in a cyclic voltammogram. For an ideal double-layer capacitor, the current flow is reversed immediately upon reversing the potential yielding a rectangular-shaped voltammogram, with a current independent of the electrode potential. For double-layer capacitors with resistive losses, the shape changes to a parallelogram. In faradaic electrodes the electrical charge stored in the capacitor is strongly dependent on the potential, therefore, the voltammetry characteristics deviate from the parallelogram due to a delay while reversing the potential, ultimately coming from kinetic charging processes.
The Newton line is the line that connects the midpoints of the two diagonals in a convex quadrilateral that is not a parallelogram. The line segments connecting the midpoints of opposite sides of a convex quadrilateral intersect in a point that lies on the Newton line.
Any line through the midpoint of a parallelogram bisects the area. All area bisectors of a circle or other ellipse go through the center, and any chords through the center bisect the area. In the case of a circle they are the diameters of the circle.
Samuelsonite is monolinic. There are three vectors of unequal length in this crystal system. The three vectors form a rectangular prism with a parallelogram at the base. Therefore, two of the vectors are perpendicular, while the third makes an angle that is not equal to 90°.
"I Don't Want To Drive You Away" was covered by Anne Murray, as "David's Song".On her What About Me album (1968). "Smoke Rings" was covered by Hiss Golden Messenger on a Parallelogram LP also featuring Michael Chapman (singer) by Three Lobed Recordings released in December 2015.
The construction shows that the parallelogram is a rhombus, which is equivalent to showing that the sums of the radii of the incircles tangent to each diagonal are equal. The quadrilateral case immediately proves the general case by induction on the set of triangulating partitions of a general polygon.
He then built off Napoleon by proving that if an equilateral triangle was constructed with equilateral triangles incident on each vertex, the midpoints of the connecting lines between the non-incident vertices of the outer three equilateral triangles create an equilateral triangle. Other similar work was done by the French Geometer Thébault in his proof that given a parallelogram and squares that lie on each side of the parallelogram, the centers of the squares create a square. Mauldon then analyzed coplanar sets of triangles, determining if they were similarity systems based on the criterion, if all but one of the triangles were directly similar, then all of the triangles are directly similar.
The number of sides of each face is twice the number of lines that cross in the arrangement. For instance, the elongated dodecahedron shown is a zonohedron with five generators, two pairs of opposite hexagon faces, and four pairs of opposite parallelogram faces. In the corresponding five-line arrangement, two triples of lines cross (corresponding to the two pairs of opposite hexagons) and the remaining four pairs of lines cross at ordinary points (corresponding to the four pairs of opposite parallelograms). An equivalent statement of the Sylvester–Gallai theorem, in terms of zonohedra, is that every zonohedron has at least one parallelogram face (counting rectangles, rhombuses, and squares as special cases of parallelograms).
The cabin is largely under the wing, with each of its side-by-side seats accessed by an upward-hinged side door. Dual control is fitted. The fuselage tapers rapidly to the rear, ending in a swept, approximately parallelogram profile fin and rudder. The Black-headed Gull has a T-tail.
Defining an aperiodic tiling (the pinwheel tiling) by repeatedly dissecting and inflating a rep-tile. Every square, rectangle, parallelogram, rhombus, or triangle is rep-4. The sphinx hexiamond (illustrated above) is rep-4 and rep-9, and is one of few known self-replicating pentagons. The Gosper island is rep-7.
The Anglo-Norman castle is positioned on a large rocky incline and it looks out over the Suir valley with the Knockmealdown Mountains to the south, and the Galtee Mountains to the northwest. The castle is a parallelogram in shape with square battlements at the corners and a fortified entrance gateway.
The underside sloped up rearwards, with an all-moving tailplane hinged at its extremity. Fin and rudder had a cropped parallelogram form, sloping up to allow clearance between rudder and elevator. The single open cockpit was ahead of the wing. Twin wheels were attached outside the fuselage, assisted by a tailskid.
We say nearly because, when a quad is something other than a perfect parallelogram (such as a rhombus or trapezoid), the surface normal would be different. Also, a quad subdivides into two or four triangles cleanly, making it easier to prepare the model for software that can only handle triangles.
"Westwood House consists of a square building, from each corner of which projects a wing in the form of a parallelogram, and turreted in the style of the Chateau de Madrid, Paris, or Holland House." —T.R. Nash History of Worcester. Westwood House is a stately home, near Droitwich, Worcestershire, England.
Boronia rhomboidea was first formally described in 1905 by William Jackson Hooker from a specimen collected by Ronald Campbell Gunn on the "side of the Western Mountains". The description was published in Icones Plantarum. The specific epithet (rhomboidea) is derived from Latin word rhombus meaning "an equilateral parallelogram with unequal pairs of angles".
In complex analysis, an elliptic function is a meromorphic function that is periodic in two directions. Just as a periodic function of a real variable is defined by its values on an interval, an elliptic function is determined by its values on a fundamental parallelogram, which then repeat in a lattice. Such a doubly periodic function cannot be holomorphic, as it would then be a bounded entire function, and by Liouville's theorem every such function must be constant. In fact, an elliptic function must have at least two poles (counting multiplicity) in a fundamental parallelogram, as it is easy to show using the periodicity that a contour integral around its boundary must vanish, implying that the residues of all simple poles must cancel.
The four "maltitudes" of a convex quadrilateral are the perpendiculars to a side through the midpoint of the opposite side, hence bisecting the latter side. If the quadrilateral is cyclic (inscribed in a circle), these maltitudes all meet at a common point called the "anticenter". Brahmagupta's theorem states that if a cyclic quadrilateral is orthodiagonal (that is, has perpendicular diagonals), then the perpendicular to a side from the point of intersection of the diagonals always goes through the midpoint of the opposite side. Varignon's theorem states that the midpoints of the sides of an arbitrary quadrilateral form the vertices of a parallelogram, and if the quadrilateral is not self-intersecting then the area of the parallelogram is half the area of the quadrilateral.
Periodic tiling by the sphinx With pentagons that are not required to be convex, additional types of tiling are possible. An example is the sphinx tiling, an aperiodic tiling formed by a pentagonal rep- tile. The sphinx may also tile the plane periodically, by fitting two sphinx tiles together to form a parallelogram and then tiling the plane by translates of this parallelogram, a pattern that can be extended to any non-convex pentagon that has two consecutive angles adding to 2, thus satisfying the condition(s) of convex Type 1 above. It is possible to divide an equilateral triangle into three congruent non-convex pentagons, meeting at the center of the triangle, and to tile the plane with the resulting three-pentagon unit.
Using the notation in the diagram on the right, the sides are (AB), (BC), (CD), (DA). But since in Euclidean geometry a parallelogram necessarily has opposite sides equal, i.e. (AB) = (CD) and (BC) = (DA), the law can be stated as : 2(AB)^2+2(BC)^2=(AC)^2+(BD)^2\, If the parallelogram is a rectangle, the two diagonals are of equal lengths (AC) = (BD), so : 2(AB)^2+2(BC)^2=2(AC)^2\, and the statement reduces to the Pythagorean theorem. For the general quadrilateral with four sides not necessarily equal, : (AB)^2+(BC)^2+(CD)^2+(DA)^2=(AC)^2+(BD)^2+4x^2, where x is the length of the line segment joining the midpoints of the diagonals.
A Besicovitch set can be created by combining three rotations of a Perron tree created from an equilateral triangle. Adapting this method further, we can construct a sequence of sets whose intersection is a Besicovitch set of measure zero. One way of doing this is to observe that if we have any parallelogram two of whose sides are on the lines x = 0 and x = 1 then we can find a union of parallelograms also with sides on these lines, whose total area is arbitrarily small and which contain translates of all lines joining a point on x = 0 to a point on x = 1 that are in the original parallelogram. This follows from a slight variation of Besicovich's construction above.
Many spaces of sequences or functions are infinite-dimensional Banach spaces. The set of all vectors of norm less than one is called the unit ball of a normed space. It is a convex, centrally symmetric set, generally not an ellipsoid; for example, it may be a polygon (in the plane) or, more generally, a polytope (in arbitrary finite dimension). The parallelogram law (called also parallelogram identity) : \lVert x-y\rVert^2 + \lVert x+y\rVert^2 = 2 \lVert x\rVert^2 + 2 \lVert y \rVert^2\ , generally fails in normed spaces, but holds for vectors in Euclidean spaces, which follows from the fact that the squared Euclidean norm of a vector is its inner product with itself, \lVert x\rVert^2 = (x, x).
This caused extremely high circulating currents and a meltdown of the transformer frame, made of metal castings and laminations. To add nighttime broadcasts, a seventh tower was added to the array. This was used with five of the existing day towers to make a new parallelogram shaped system. KLAT began night operation at 1,000 watts.
Parabola (magenta) and line (lower light blue) including a chord (blue). The area enclosed between them is in pink. The chord itself ends at the points where the line intersects the parabola. The area enclosed between a parabola and a chord (see diagram) is two-thirds of the area of a parallelogram that surrounds it.
In 1998 the Sfida 1000 4V was introduced. The 102 bhp 4 valve 992 cc Moto Guzzi Daytona engine was fitted and the bike used a monoshock version of the parallelogram rear suspension. Side panels were made of carbon-fibre. As with previous Sfida models, cafe-racer tank, humped seat and half-fairing were fitted.
It was designed by architects Louis Kamper and Paul Kamper for Theodore Eaton. The tower is located at the Southeast corner of Woodward Avenue and Witherell Street, facing Grand Circus Park, and stands across the street from the David Whitney Building. The Broderick Tower is not a square, or even a parallelogram in shape.
Cylindric section A cylindric section is the intersection of a cylinder's surface with a plane. They are, in general, curves and are special types of plane sections. The cylindric section by a plane that contains two elements of a cylinder is a parallelogram. Such a cylindric section of a right cylinder is a rectangle.
In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles. It can also be defined as an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°). It can also be defined as a parallelogram containing a right angle. A rectangle with four sides of equal length is a square.
Wright designed the house around a "diamond module" with 60- and 120-degree angles. The red cement floors had a diamond pattern in the same shape. The skylights were equilateral triangles, each corner 60 degrees. The pool, nestled into the wide corner of the L-shaped house, was a parallelogram with a notch out of one corner.
An anti­parallelogram In geometry, an antiparallelogram is a quadrilateral having, like a parallelogram, two opposite pairs of equal-length sides, but in which the sides of one pair cross each other as in a scissors mechanism. The longer of the two pairs will always be the one that crosses. Antiparallelograms are also called contraparallelograms. or crossed parallelograms.
There are two main plazas. The larger is called del Olmo, an ample, irregular polygon, where the weekly market and the annual fair are held. The smaller plaza, adjacent to the chapel, is a parallelogram of 11 m x 7 m dimension. There are three smaller plazas called del Loreto, Tiendas (shops), and Carnicerías (meat markets).
Sky Arrow is TV guided like LMD-002.Sky Arrow UAV employed missile The aerodynamic layout of Sky Arrow contains four pairs of control surfaces, with four parallelogram shaped ones in front, and four smaller trapezoid shaped ones in the tail, and the missile uses rocket motor instead of turbojet engine and thus does not have any intake.
Theoretically, a complete description of the path and position at each instant of time may be deduced when the velocity in any one position and the acceleration for all positions is given. # The parallelogram law as the general rule for combining motions is the foundation of the synthesis by which complex motions are constructed out of simple motions.
Monoclinic crystal An example of the monoclinic crystal orthoclase In crystallography, the monoclinic crystal system is one of the seven crystal systems. A crystal system is described by three vectors. In the monoclinic system, the crystal is described by vectors of unequal lengths, as in the orthorhombic system. They form a rectangular prism with a parallelogram as its base.
By the above proof, they are equivalent to a single velocity, Fnet. By Newton's second law, this vector is also a measure of the force which would produce that velocity, thus the two forces are equivalent to a single force. Routh (1896), p. 14 Using a parallelogram to add the forces acting on a particle on a smooth slope.
For objects with several symmetries, the center of symmetry is the point left unchanged by the symmetric actions. So the center of a square, rectangle, rhombus or parallelogram is where the diagonals intersect, this being (amongst other properties) the fixed point of rotational symmetries. Similarly the center of an ellipse or a hyperbola is where the axes intersect.
The required point is where this line intersects the parabola. Then, using the formula given in Distance from a point to a line, calculate the perpendicular distance from this point to the chord. Multiply this by the length of the chord to get the area of the parallelogram, then by 2/3 to get the required enclosed area.
Charles Isherwood, in his review in The New York Times, called it an "acidic satire of bourgeois venality and hypocrisy."Isherwood, Charles. "The Rich and Faithful in Africa. Discuss.", The New York Times, May 22, 2007 A Parallelogram was produced at Steppenwolf Downstairs Theatre from July 1 through August 29, 2010, directed by Anna D. Shapiro.
Directed by Michael Grief, the cast features Celia Keenan-Bolger, Anita Gillette, Stephen Kunken and Juan Castano. McBride, Walter. "Photo Coverage: The Company of 'A Parallelogram' Celebrates Opening Night!" broadwayworld.com, August 3, 2017 Domesticated had its world premiere Off-Broadway at the Lincoln Center Mitzi E. Newhouse Theater, running from October 10, 2013 (previews) to January 5, 2014.
The building is a parallelogram with a 120 ft. of frontage on Center St. with a depth of 80 ft. The height to the eaves of the roof is 48 ft. Eighty thousand pressed bricks made by H & G Evans of Philadelphia were used to construct the outer walls, and 20,000 bricks were made onsite for the inner walls.
But 2 channels sometimes are not enough for use. 2-channel filter banks can be cascaded to generate multi-channel filter banks. Four possible parallelogram supports of the two channel filter bank To understand the working of 2-Channel Multidimensional filter banks we must first understand the design process of a simple 2D two-channel filter banks.
This instrument is first attested in accounts dated 1730. The primitive version with four strings evolved into a five-string model. The Val-d'Ajol épinette is of small size, between 50 and 60 cm, in the form of a parallelogram with a wide base. The frets, originally numbering fourteen, increased to seventeen in the 19th century.
However, the thickening remains limited. With the third metatarsal, the innermost lower joint bump is the largest. With the remarkably robust fourth metatarsal leg, the upper outer edge forms a sharp ledge; at Talenkauen, Morrosaurus and the Styracosterna this piece is completed. The bottom surface forms a parallelogram whose rear edge protrudes more inwards but is curled outwards.
The decomposable k-vectors have geometric interpretations: the bivector represents the plane spanned by the vectors, "weighted" with a number, given by the area of the oriented parallelogram with sides u and v. Analogously, the 3-vector represents the spanned 3-space weighted by the volume of the oriented parallelepiped with edges u, v, and w.
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.
For instance, :dx^1\wedge dx^2=-dx^2\wedge dx^1 because the square whose first side is and second side is is to be regarded as having the opposite orientation as the square whose first side is and whose second side is . This is why we only need to sum over expressions , with ; for example: . The exterior product allows higher-degree differential forms to be built out of lower-degree ones, in much the same way that the cross product in vector calculus allows one to compute the area vector of a parallelogram from vectors pointing up the two sides. Alternating also implies that , in the same way that the cross product of parallel vectors, whose magnitude is the area of the parallelogram spanned by those vectors, is zero.
1901 Tullio Campagnolo born on 26 August in the eastern suburbs of Vicenza, Italy 1922 Tullio Campagnolo begins his racing career 1930 Campagnolo patents the quick-release hub 1933 After fabricating parts in the backroom of his father's hardware store, Tullio starts Campagnolo SPA with production of the quick-release hub 1940 Tullio hires his first full- time employee. The derailleur enters production, enabling gears to change without removing the wheel. The pieces are handmade 1949 Campagnolo introduces a parallelogram rear derailleur, the Gran Sport Gran Sport rear derailleur 1956 Campagnolo introduces a parallelogram front derailleur 1963 The Record rear derailleur (chromed bronze) is introduced 1966 The Nuovo Record rear derailleur is introduced. Eddy Merckx uses it for his first four Tour de France victories 1973 The Super Record Road and Track groups are introduced.
The precise date as to when the castle was built is unknown. However, it was most probably built in the 11th or the early 12th century. The ground plan of the castle is in the shape of a parallelogram, which houses two courts, one of which is square in form. The motte most probably had a wooden tower and a palisade.
The trusses include wrought iron rods, and are set at an offset to one another, giving the bridge the shape of a parallelogram. A laminated beam has been bolted to the underside of the floor planking to provide additional strength. The bridge is long and wide, with a roadway width of (one lane). with The bridge was built c. 1886-87.
Watt's parallel motion generator consists of the four-bar linkage that has a coupler curve that traces an approximately straight line trajectory, combined with a parallelogram linkage that copies this straight line movement to a desired location. This configuration of a six bars and seven joints has two four-bar loops. A six-bar linkage with a rectilinear moving link. Click to enlarge.
A parallelogon must have an even number of sides and opposite sides must be equal in length and parallel (hence the name). A less obvious corollary is that all parallelogons have either four or six sides; a four-sided parallelogon is called a parallelogram. In general a parallelogon has 180-degree rotational symmetry around its center. The faces of a parallelohedron are parallelogons.
All triangles are affine-regular. In other words, all triangles can be generated by applying affine transformations to an equilateral triangle. A quadrilateral is affine-regular if and only if it is a parallelogram, which includes rectangles and rhombuses as well as squares. In fact, affine-regular polygons may be considered a natural generalization of parallelograms.. See in particular p. 249.
Book one contains fifteen propositions with seven postulates. In proposition six Archimedes establishes the law of the lever, concluding that "Magnitudes are in equilibrium at distances reciprocally proportional to their weights." In propositions ten and fourteen, respectively, Archimedes locates the centre of gravity of the parallelogram and the triangle. Additionally, in proposition 15, he establishes the centre of gravity of the trapezium.
The District is roughly a parallelogram in shape and lies between Latitude 26°8' N & 27°2' N and Longitude 80°3' E & 81°3' E. It is bounded on the North by District Hardoi, on the East by District Lucknow, on the South by District Rae Bareli and on the West by the Ganga which separates it from districts of Kanpur & Fatehpur.
The aerodynamics of current FIA Formula 3 Championship cars are resembling the Formula One 2017-style aerodynamic with wider and curved front wing and also lower rear wing with parallelogram rear wing plate. Side winglets are also banned. The undertrays of all FIA Formula 3 Championship cars are grounds-effect underbody as opposed to flat-bottom underbody that usually utilized in Formula One.
Thin section of a mica fish in mylonitic quartzite from the Italian Alps Mica fish are lenticular, elongate lozenge, parallelogram-shaped, or lens-shaped (roughly fish-shaped) single mica crystals that are often used as shear sense indicators.Mica fish in mylonites They commonly occur in micaceous quartzitic mylonites. They characteristically lie with their longest dimension at a small angle to the mylonitic foliation.
Proof of Apollonius's theorem The theorem can be proved as a special case of Stewart's theorem, or can be proved using vectors (see parallelogram law). The following is an independent proof using the law of cosines. Let the triangle have sides with a median drawn to side . Let be the length of the segments of formed by the median, so is half of .
Limerick provided the opposition on that occasion and an entertaining contest unfolded. New rules regarding the parallelogram confused the players and Limerick had two goals disallowed because of a ‘square ball.’ Wexford had a goal disallowed for the same reason; however, they still went on to win the game by 7-0 to 6-2. It was Mackey’s first All-Ireland medal.
Ruins of Pataliputra at Kumhrar. Though parts of the ancient city have been excavated, much of it still lies buried beneath modern Patna. Various locations have been excavated, including Kumhrar, Bulandi Bagh and Agam Kuan. During the Mauryan period, the city was described as being shaped as parallelogram, approximately 2.5 kilometers (1.5 miles) wide and 15 kilometers (9 miles) long.
Euclid introduced the term in his Elements in Book I, Definition 22, Euclid never used the definition of rhomboid again and introduced the word parallelogram in Proposition 34 of Book I; "In parallelogrammic areas the opposite sides and angles are equal to one another, and the diameter bisects the areas." Heath suggests that rhomboid was an older term already in use.
Page 27. This centralized parallelogram-shaped building is the oldest example of the cross-in-square type in the country; its plan closely follows that of Lips Monastery in Constantinople. The walls are opus mixtum (part brick, part stone, part marble) and display curious pseudo- kufic patterns. The Hosios Loukas adjoins a larger cathedral church, or Katholikon, tentatively dated to 1011-12.
In the geometrical and physical settings, it is sometimes possible to associate, in a natural way, a length or magnitude and a direction to vectors. In addition, the notion of direction is strictly associated with the notion of an angle between two vectors. If the dot product of two vectors is defined—a scalar-valued product of two vectors—then it is also possible to define a length; the dot product gives a convenient algebraic characterization of both angle (a function of the dot product between any two non-zero vectors) and length (the square root of the dot product of a vector by itself). In three dimensions, it is further possible to define the cross product, which supplies an algebraic characterization of the area and orientation in space of the parallelogram defined by two vectors (used as sides of the parallelogram).
Stadttor () is a 20-storey skyscraper in Unterbilk neighborhood of Düsseldorf, Germany. The building was designed by Düsseldorf-based architecture firm Petzinka, Overdiek und Partner and completed in 1998. It marks the Southern entrance of Rheinufertunnel, which is also reason for its parallelogram-shaped floor plan. The building features a 15-story atrium and a double-facades, allowing natural ventilation even on higher elevation floors.
Metatarsal I is somewhat squashed diagonally, with the edge facing the rest of the foot being positioned higher than the inner edge. A crest is also present on the inner edge. The articulation with the ankle is convex and expanded towards the rest of the foot. Metatarsal II is parallelogram-shaped in cross section, with a 'lip' on its upper edge that accepts the first metatarsal.
Addition of two complex numbers can be done geometrically by constructing a parallelogram. Two complex numbers a and b are most easily added by separately adding their real and imaginary parts of the summands. That is to say: :a + b =(x+yi) + (u+vi) = (x+u) + (y+v)i. Similarly, subtraction can be performed as :a - b =(x+yi) - (u+vi) = (x-u) + (y-v)i.
Suspension seatposts allow the saddle to move up and down with either a telescoping or parallelogram mechanism and incorporate a spring, an elastomer, or compressed air and possibly a damper to insulate against bumps. The preload of the spring may be adjustable. These seatposts are most common on hybrid and mountain bikes. Suspension seatposts usually come in fewer diameters, and shims are more likely to be necessary.
Targeting towers use a special device to ensure an antenna's stability when strong wind blows. This system is based on the geometrical properties of the parallelogram. Three vertical rods are used to maintain the top platform horizontal when the tower bends under the wind effect. The top platform is pin connected to the mast, thanks to a special mechanical link based on universal joint system.
All Deutsche Tourenwagen Masters cars aero packages are completely assembled. The car floor underbody is flat. Serratured side front fenders are included along with triple-decker front side winglet flicks, multiple side winglet flicks and multiple rear winglet flicks. The 2017-2018 generation of rear wing for all Deutsche Tourenwagen Masters cars are slightly wider, bi-plane wing and also parallelogram rear wing end plate.
In 1933, the first quick release hubs were produced by Campagnolo. Also in 1933, he patented the sliding hub, dual seatstay rod-operated, back-pedal derailleur, ultimately known as the 'Cambio Corsa'. In 1949, he introduced the 'Gran Sport' twin-cable, parallelogram rear derailleur at the Milan trade show, the first modern derailleur. Campagnolo was also an innovator in materials engineering for bicycle component design.
One side of the parallelogram is the chord, and the opposite side is a tangent to the parabola. The slope of the other parallel sides is irrelevant to the area. Often, as here, they are drawn parallel with the parabola's axis of symmetry, but this is arbitrary. A theorem equivalent to this one, but different in details, was derived by Archimedes in the 3rd century BCE.
This view allows for a natural geometric interpretation of the cross product. In exterior algebra the exterior product of two vectors is a bivector. A bivector is an oriented plane element, in much the same way that a vector is an oriented line element. Given two vectors a and b, one can view the bivector as the oriented parallelogram spanned by a and b.
Earlier, fort wall had a thickness of 1.9 meters, which was raised to 3.7–4.1 meters during reconstruction in this phase. Brick size was 20 × 20 × 10 cm in both construction-phases. The citadel mound (smaller mound) is a parallelogram about 130 meters on the east-west axis and 260 meters on the north-south. Town planning was like that of Mohenjodaro or Harappa.
Specifically, let be an arbitrary cyclic quadrilateral and let , , , be the incenters of the triangles , , , . Then the quadrilateral formed by , , , is a rectangle. Note that this theorem is easily extended to prove the Japanese theorem for cyclic polygons. To prove the quadrilateral case, simply construct the parallelogram tangent to the corners of the constructed rectangle, with sides parallel to the diagonals of the quadrilateral.
He tours regularly across the USA, Latin America and Ireland with guitarist William Coulter "Luck o' the Irish" , Pasadena Weekly, 24 September 2009; retrieved 17 August 2017. with whom he released the EP 'Toward the Sun' in 2015. He also plays with an influential Russian rock group Aquarium, both live and on their studio albums (since approximately 2009). He worked on cross genre project Parallelogram.
A geometric diagram of the basic principle of a pop-up book: the parallelogram. Design and creation of such books in arts is sometimes called "paper engineering". This usage should not be confused with traditional paper engineering, the engineering of systems to mass-produce paper products. The artistic aspect of paper engineering is related to origami in that the two arts both employ folded paper.
Each proposition is illustrated with a crudely drawn diagram. Several lines of text in each proposition were left shorter than the remainder of the text lines in order to leave space in the right of the column for the illustrations. The left column has a parallelogram, and two right-angled triangles, while the right has an equilateral triangle, a stone, and two concentric circles.
The current castle building forms a punctuated regular parallelogram. The Renaissance Italian architect who designed the castle added a line of trees to shelter the castle from inquisitive eyes. Once past the long alley bordered with lime and chestnut trees, one lands on the main courtyard of the castle. The eye-shaped courtyard contains a fountain with a double basin and a majestic well.
Nestlé then approached Manhattanville College, which had recently announced plans to sell of surplus land from its campus. With subsequent state modifications to the I-684 highway to the site, it became possible for the construction of the headquarters. By 1980 Nestlé had commissioned renowned architect I. M. Pei to design the building, which would be composed of a central saw-toothed parallelogram and two quarter-circle wings.
For its first year of coverage in 1996, Fox used the scoring bug on their Major League Baseball telecasts. Within two years, the bug would be expanded to all sports telecasts on Fox and other networks. The first scoring bug was a translucent parallelogram with red borders on the left and right. The Fox logo and inning were on the left side, with the score on the right side.
In contrast, the perimeter (relative to the taxicab metric) of the unit disk in the taxicab geometry is 8. In 1932, Stanisław Gołąb proved that in metrics arising from a norm, the perimeter of the unit disk can take any value in between 6 and 8, and that these extremal values are obtained if and only if the unit disk is a regular hexagon or a parallelogram, respectively.
The city was also under latent danger of attack by the Venetians. For centuries the people of Dubrovnik were able to preserve their city-republic by skillful maneuvering between East and West. A strategic treaty with Turkey protected Ragusa's liberty and maintained the opportunity for a major trading role between the Ottoman Empire and Europe. The irregular parallelogram surrounding Dubrovnik consists of four strong fortresses at its most significant points.
The form of the main building at Milwaukee was a parallelogram, exclusive of an extension at each end in octagonal form, measuring , and a one-story addition in the rear for laundry and cellar purposes, . It was three stories high above the basement. The building afforded ample accommodation for 200 pupils, plus teachers, resident officers, and assistants. The house was well ventilated, and provision was made for warming it.
According to Lanciani the foundations of the temple were discovered in March 1881, under what was formerly the convent of S. Silvestro al Quirinale (or degli Arcioni), later the headquarters of the (former) Royal Engineers. Lanciani relates the monument was a parallelogram in shape, thirty-five feet long by nineteen wide, with walls of travertine and decorations in white marble. It was surrounded by votive altars and the pedestal of statues.
To the west of the lagoon's mouth is the prominent headland of Lawyers Head, a major Dunedin landmark. The outer lobe (the Bottom Lagoon) is the larger, being some in length and wide at its widest point. It is roughly a parallelogram in shape, and covers an area of close to . The Top Lagoon joins the Bottom Lagoon via a short stream in the middle of the latter's eastern shore.
The height of this parallelogram is , and the width is half the circumference of the circle, or . Thus, the total area of the circle is : : (circle). Though the dissection used in this formula is only approximate, the error becomes smaller and smaller as the circle is partitioned into more and more sectors. The limit of the areas of the approximate parallelograms is exactly , which is the area of the circle.
A 90 m grass path leads from this road to the entrance. The cemetery was designed by Noel Rew and has the shape of a parallelogram with an area of approximately 967 m². It is bordered on three sides by a low natural stone wall, the southern boundary is delimited by a hedge. In a semicircular indentation of the wall there is a metal gate between two columns for access.
The island is roughly a parallelogram in shape, with long east and west coasts and shorter coasts facing northwest and southeast. It is approximately in width, and its maximum length is , between Cape Freeman in the north and Cape Smyth in the south. It is covered by ice and snow all the year around. The island's highest point reaches Brown Peak, Composite Gazetteer of Antarctica, Scientific Committee on Antarctic Research.
There is some disagreement whether parallelograms, which have two pairs of parallel sides, should be regarded as trapezoids. Some define a trapezoid as a quadrilateral having only one pair of parallel sides (the exclusive definition), thereby excluding parallelograms. Others define a trapezoid as a quadrilateral with at least one pair of parallel sides (the inclusive definitionTrapezoids, . Retrieved 2012-02-24.), making the parallelogram a special type of trapezoid.
Arms of Denys Sir Robert Denys (1525–1592), MP, built a mansion house near the site of the present Orangery, now within the Bicton Botanical Gardens. He was the son of Sir Thomas Denys (died 1561), Sheriff Of Devon, Privy Councillor and Chancellor to Anne of Cleves. He received a royal licence to empark, and stocked his new park with deer. He added formal gardens with slopes, terraces and parallelogram ponds.
An automedian triangle is one whose medians are in the same proportions as its sides (though in a different order). If ABC is an automedian triangle in which vertex A stands opposite the side a, G is the centroid (where the three medians of ABC intersect), and AL is one of the extended medians of ABC with L lying on the circumcircle of ABC, then BGCL is a parallelogram.
The entrance to all the shops is off of an angular ramp that wraps around an open parallelogram as it leads upward to the shops. Four shops were envisioned with the penthouse space, an apartment. Like the Marin Civic Center, this is another example of a secular Wright building with a "steeple". The inverted “V” front elevation stands out in sharp contrast to its traditional, flat- front urban neighbors.
The Wigner–Seitz cell, named after Eugene Wigner and Frederick Seitz, is a primitive cell which has been constructed by applying Voronoi decomposition to a crystal lattice. It is used in the study of crystalline materials in solid- state physics. Wigner–Seitz primitive cell for different angle parallelogram lattices. The unique property of a crystal is that its atoms are arranged in a regular three-dimensional array called a lattice.
An inner product space is a real or complex linear space, endowed with a bilinear or respectively sesquilinear form, satisfying some conditions and called an inner product. Every inner product space is also a normed space. A normed space underlies an inner product space if and only if it satisfies the parallelogram law, or equivalently, if its unit ball is an ellipsoid. Angles between vectors are defined in inner product spaces.
By the mid-20th century, annexes had been added to both buildings, giving them a combined lot area of . The two buildings were otherwise designed similarly. The first through third stories of both buildings were parallelogram in plan, while the buildings contained "H"-shaped floor plans above the third story. The light courts of both buildings faced north and south, while the main corridors of each level on both buildings extended eastward from Church Street.
Instead of using individual DX tiles, a single long scaffold strand is folded into the desired shape by a number of short staple strands. When assembled, the scaffold strand is continuous through the double-helical domains, while the staple strands participate in the Holliday junctions as crossover strands. Some tile types that retain the Holliday junction's native 60° angle have been demonstrated. One such array uses tiles containing four Holliday junctions in a parallelogram arrangement.
Vladimir Putin stands at the entrance to the Jewish Museum in 2018. According to a May 2014 article by Alexis Zimberg in the Calvert Journal, the new Jewish Museum occupies the restored Bakhmetevsky Bus Garage. The 8,500-square-metre space is a landmark of the avant-garde 1920s. Designed by architect Konstantin Melnikov and structural engineer Vladimir Shukhov in 1926, the angled parallelogram building went from blueprint to structure in just one year.
By the late 1990s, a brighter logo—still with a gold '5'—returned to the rectangular look, adding a black ABC logo. From 2004 to late 2014, a white '5' was used on a red parallelogram, also featuring the ABC logo. On November 30, 2014, the logo was redesigned, and now features the "groovy 5" logo in blue with red lines circling the left part of the logo, with the ABC logo again.
In 1896 Stevenson published The Square of Sevens, and the Parallelogram: An Authoritative Method of Cartomancy with a Prefatory Note by Robert Antrobus that was supposedly written in 1735. However, it is believed that he was the author. In 1906, under the pseudonym Xavier Mayne, Stevenson published the homosexually themed novel Imre: A Memorandum, and in 1908 a sexology study, The Intersexes, a defense of homosexuality from a scientific, legal, historical, and personal perspective.
The drivers had to use two pedals to shift: upshift on one side and downshift on the other. A parallelogram fork was used at the rear, which would have been useful to keep chain tension constant, but was not an advantage with shaft drive. The fork was equipped with torsion suspension and friction dampers. The frame was a double cradle, of which the front part was made from tubing and the rear pressed sheet metal.
The Berici Hills stand out, south of Vicenza, with the shape of a parallelogram, whose major axis is oriented towards the Northeast. It is about , and with a total area of about 165 km². The profile is evenly curved, compact and not particularly high on the level of the plain. The edges are jagged enough on each side, with alternating indentations and sinuosity or with simple engravings on the sides, the "scaranti".
A self-made man, Wright respected him and allowed him to design many details including all door hardware, the stainless steel kitchenettes and even the diving board support. This sprawling Usonian is one of Wright's most extensive single-story residences. Three wings spin off a central hexagon much as might have happened had Wingspread been based on an equilateral parallelogram rather than a square. The home is organized around a massive angular fireplace.
An alternative to the unit cell, for every Bravais lattice there is another kind of primitive cell called the Wigner–Seitz cell. In the Wigner–Seitz cell, the lattice point is at the center of the cell, and for most Bravais lattices, the shape is not a parallelogram or parallelepiped. This is a type of Voronoi cell. The Wigner–Seitz cell of the reciprocal lattice in momentum space is called the Brillouin zone.
1910 saw the first ever championship meeting of Wexford and Limerick, as both sides contested the All-Ireland final. The introduction of new rules regarding the ‘parallelogram’ seemed to confuse players and officials. Limerick had a goal disallowed for this reason while Wexford's eighth goal was also ruled out for the same reason. The final was a close game; however, Wexford claimed their first title on a score line of 7–0 to 6–2.
The converse is also true: a circle can be inscribed into every quadrilateral in which the lengths of opposite sides sum to the same value.Alexander Bogomolny "When A Quadrilateral Is Inscriptible?" at Cut-the- knot This theorem and its converse have various uses. For example, they show immediately that no rectangle can have an inscribed circle unless it is a square, and that every rhombus has an inscribed circle, whereas a general parallelogram does not.
In the United States, many states distinguish their license plates through distinctive color schemes and logos, which persist over time. For example, the cowboy logo often associated with the state of Wyoming has appeared on that state's license plates continuously since 1936. Some early Tennessee plates were produced in a parallelogram shape approximating that of the state. Arizona has had the slogan "Grand Canyon State" on its license plates since the 1930s.
The south side of the bridge has two square window holes, which improve visibility due to a sharp turn in the road at one end. The trusses are set at a skew, giving the bridge the shape of a parallelogram. The portals are square, and the exterior sheathing extends around to the ends of the trusses on the interior. with The bridge was built in 1883, and has been little altered since then.
The first sign of trouble came with returns on SunTour's SR MounTech rear derailleur, caused by failures of the innovative spring-loaded jockey wheel that was fitted with a seal that proved inadequate to keep out dirt and mud. In road bicycle components, the company fared no better. SunTour had introduced the SuperbeTech derailleur in 1983 with a streamlined, enclosed parallelogram. However, the design was too fragile, with internal pivots and the return spring failing frequently.
The isoperimetric theorem for rectangles states that among all rectangles of a given perimeter, the square has the largest area. The midpoints of the sides of any quadrilateral with perpendicular diagonals form a rectangle. A parallelogram with equal diagonals is a rectangle. The Japanese theorem for cyclic quadrilateralsCyclic Quadrilateral Incentre-Rectangle with interactive animation illustrating a rectangle that becomes a 'crossed rectangle', making a good case for regarding a 'crossed rectangle' as a type of rectangle.
Lucien Charles Hippolyte Juy was a French industrialist who made derailleur gears. He is credited with making the first derailleur with a collapsible parallelogram. A hinged frame swung in and out from the frame and fed the chain to one of a number of sprockets attached to the hub. Juy's derailleurs, sold as Simplex derailleurs, were novel in having a jockey wheel to correct the tension of the chain as it moved across differently sized sprockets.
The city is built in the shape of a parallelogram and the area within the walls is about . This walled city is slightly elevated hence protecting it from destruction and any outside invasion. It was Akbar who, during his stay in Lahore, built a brick wall around the city to protect it. Since the walls had decayed over time, when Ranjit Singh came into power afterwards he rebuilt these walls and added a deep broad ditch around.
See theorems 5.1 and 5.2 of . However, every graph of maximum degree three has slope number at most four;, improving an earlier result of ; theorem 5.3 of . the result of for the complete graph shows that this is tight. Not every set of four slopes is suitable for drawing all degree-3 graphs: a set of slopes is suitable for this purpose if and only it forms the slopes of the sides and diagonals of a parallelogram.
The Ivan Franko Park (Lviv, Ukraine) is located on a hillside of the Lviv Heights between Lystopadovoho Chynu and Krushelnytskoi Streets. It is near Lviv University, which is also named after Ivan Franko. The park fills a parallelogram between Marshalkovska, Mitskevych, Mateyko and Krashevsky Streets (presently, Universitetska, Lystopadovoho Chynu, Mateyko, and Krushelnytskoi) (Miasto Lwów, 1896, 318) A large statue of Ivan Franko towers over the parkJozef Wittlin, Philippe Sands, City of Lions, Books.google.fr, 21 March 2017.
The neck vertebrae are parallelogram- shaped and moderately elongated, proportionally similar to other silesaurids. Most of the depressions and ridges on the neck vertebrae of Asilisaurus were not as well-developed as those of Silesaurus. However, the postzygapophyses of a few vertebrae do have small projections identified as epipophyses, which are present in aphanosaurs and dinosaurs but not advanced silesaurids. The dorsal vertebrae are shorter and more complex, lacking epipophyses and instead possessing hyposphenes, another dinosaur-like feature.
Schematic of Watt's parallel motion: A and G are fixed hinge joints while F is not a joint but merely signifies the point on the linkage which follows a lemniscate. Its motion is magnified in D by the parallelogram BCDE. See the diagram on the right. A is the journal (bearing) of the walking beam KAC, which rocks up and down about A. H is the piston, which is required to move vertically but not horizontally.
Mountain coral heath was first formally described in 1810 by Lilian Fraser and Joyce Vickery, who gave it the name Epacris microphylla var. rhombifolia. The description was published in Journal and Proceedings of the Linnean Society of New South Wales. The variety was raised to species level in 2015 by Yvonne Menadue and Ron Crowden. The specific epithet (rhombifolia) is derived from the Latin words rhombus meaning "an equilateral parallelogram with unequal pairs of angles" and folium meaning "leaf".
The name of standard models varies during the years, which could be simply Hummingbird with no suffix, Hummingbird Modern Classic or Hummingbird Standard. They often have AA or AAA-grade solid Sitka spruce tops, with mahogany back and sides. A Hummingbird of this category features a rosewood fretboard with double parallelogram inlays, a crown peghead inlay headstock, nickel Grover rotomatic tuners and a custom-made Hummingbird tortoiseshell pickguard. An L.R. Baggs Element Active pickup system is also installed.
The Wellington Independent, in describing St Mary's Cathedral when its extensions were nearing completion in December 1867, stated that the original building opened in 1851 was lengthened by 33 feet and that the early English Gothic or decorated style had been adopted. The building was in the form of a parallelogram with a "lofty and imposing" tower in the southeast corner. This replaced the original tower. The cathedral measured 108 feet in length and 58 feet in width.
The Penitentiary's design is similar to the facility at the 1858 state prison in Joliet, Illinois, with its castellated Gothic, stone structure, complete with turrets and battlements, except it is scaled down to half the size. The original architectural designs have been lost. The dimensions of the parallelogram-shaped prison yard are 82½ feet in length, by 352½ feet in width. The stone walls are thick at the base, tapering to 2½ feet at the top, with foundations deep.
A corollary to Euler's quadrilateral theorem is the inequality : a^2 + b^2 + c^2 + d^2 \ge p^2 + q^2 where equality holds if and only if the quadrilateral is a parallelogram. Euler also generalized Ptolemy's theorem, which is an equality in a cyclic quadrilateral, into an inequality for a convex quadrilateral. It states that : pq \le ac + bd where there is equality if and only if the quadrilateral is cyclic. This is often called Ptolemy's inequality.
The engine compartment was located in the middle of the hull and the tank was powered by a V8 gasoline engine. Features of the design were adopted from the British Vickers A1E1 Independent tank. The tank chassis had a complex parallelogram suspension system with two pairs of road bogie wheels per leaf spring arrangement. Hara later designed a bell crank scissors suspension which paired the bogie wheels and connected them to a coil spring mounted horizontally outside the hull.
The fin and rudder formed a tilted, cropped parallelogram with a hinge line above that of the elevator. The cockpit was immediately under the leading edge, well behind the nose. Originally the Phi-Phi had a pair of small main wheels rigidly attached to the lower fuselage directly below the cockpit and aided by a sprung, articulated tailskid. The wheels were replaced at Itford by a pair of skids and then by skids with small wheels attached to them.
As with the rear derailleur, the front derailleur has a cage through which the chain passes. On a properly adjusted derailleur, the chain will only touch the cage while shifting. The cage is held in place by a movable arm which is usually implemented with a parallelogram mechanism to keep the cage properly aligned with the chain as it swings back and forth. There are usually two adjustment screws controlling the limits of lateral travel allowed.
The South Superior Union Hall was built in 1921 in the southern part of what is now Superior, Wyoming. The hall was built by six locals of the United Mine Workers to accommodate union and community activities in the coal-mining community of Superior. Built in 1921, the two-story brick hall's plan is a parallelogram, though to be unique for its time in Wyoming. The hall housed doctors' and dentists' offices, a bowling alley and a grocery store.
Wiseman, pp. 140 and 145. After the firm's first plan was discarded due to a need for more office space, Cobb developed a new plan around a towering parallelogram, slanted away from the Trinity Church and accented by a wedge cut into each narrow side. To minimize the visual impact, the building was covered in large reflective glass panels; Cobb said this would make the building a "background and foil" to the older structures around it.
In this sense, the scale was revolutionary: it evolved into the more-commonly encountered form consisting of two pans placed on vertical column located above the fulcrum and the parallelogram below them. The advantage of the Roberval design is that no matter where equal weights are placed in the pans, the scale will still balance. A gear balance:A rare document on "gear balance". A = Axle, F = Frame, G = Generator, GL = geared linkage, WL = weighted lever; counter weight added for balance, all the gear linkages free running on the rotating frameFurther developments have included a "gear balance" in which the parallelogram is replaced by any odd number of interlocking gears greater than one, with alternating gears of the same size and with the central gear fixed to a stand and the outside gears fixed to pans, as well as the "sprocket gear balance" consisting of a bicycle-type chain looped around an odd number of sprockets with the central one fixed and the outermost two free to pivot and attached to a pan.
For a convex quadrilateral with sides a, b, c, d, diagonals e and f, and g being the line segment connecting the midpoints of the two diagonals, the following equations holds: :a^2+b^2+c^2+d^2=e^2+f^2+4g^2 If the quadrilateral is a parallelogram, then the midpoints of the diagonals coincide so that the connecting line segment g has length 0. In addition the parallel sides are of equal length, hence Euler's theorem reduces to :2a^2+2b^2=e^2+f^2 which is the parallelogram law. If the quadrilateral is rectangle, then equation simplifies further since now the two diagonals are of equal length as well: :2a^2+2b^2=2e^2 Dividing by 2 yields the Euler–Pythagoras theorem: :a^2+b^2=e^2 In other words, in the case of a rectangle the relation of the quadrilateral's sides and its diagonals is described by the Pythagorean theorem.Lokenath Debnath: The Legacy of Leonhard Euler: A Tricentennial Tribute.
Zijlpoort Zijlpoort is a city gate in Leiden, The Netherlands. The gate was built in 1667 in the classical style according to a design by the Leiden architect Willem van der Helm and with sculpture by Rombout Verhulst. Because the gates have to connect with the city wall as well as with a bridge, the building is in the form of a parallelogram. The Zijlpoort, together with the Morspoort (1669) and Doelenpoort (1645), are the only of the original eight gates that survived.
The instrument for double writing was one of the first attempts of Petty to make money with an invention. Already early in 1603, a Bavarian Jesuit priest, Christoph Scheiner (1573-1650) had invented a pantograph, a mechanical instrument, in which a pencil was connected to a stylus by means of a parallelogram. The pantograph was intended to create a copy of an image. Scheiner's invention was described in his Pantographice seu Ars delineandi res quaslibet per parallelogrammum lineare seu cavum (1631).
Pevsner, The Buildings of England: Nottinghamshire, 2nd edition revised by E. Williamson (1979), p. 89. An organ chamber was built in 1888 and an annexe in 1962. The nave has the somewhat unusual form of a wide parallelogram 42 feet 8 inches long and 37 feet 2 inches wide, of one span and with no traces of any arcades. The chancel arch is not in the centre of the east wall of the nave, but about five feet nearer to the north side.
The hyperplanes of a three-dimensional space are the two-dimensional subspaces, that is, the planes. In terms of Cartesian coordinates, the points of a hyperplane satisfy a single linear equation, so planes in this 3-space are described by linear equations. A line can be described by a pair of independent linear equations—each representing a plane having this line as a common intersection. Varignon's theorem states that the midpoints of any quadrilateral in ℝ3 form a parallelogram, and hence are coplanar.
Graphs are drawn as rods connected by rotating hinges. The cycle graph C4 drawn as a square can be tilted over by the blue force into a parallelogram, so it is a flexible graph. K3, drawn as a triangle, cannot be altered by any force that is applied to it, so it is a rigid graph. In discrete geometry and mechanics, structural rigidity is a combinatorial theory for predicting the flexibility of ensembles formed by rigid bodies connected by flexible linkages or hinges.
Newton's diagram (also known as Newton's parallelogram, after Isaac Newton) is a technique for determining the shape of an algebraic curve close to and far away from the origin. It consists of plotting (α, β) for each term Axαyβ in the equation of the curve. The resulting diagram is then analyzed to produce information about the curve. Specifically, draw a diagonal line connecting two points on the diagram so that every other point is either on or to the right and above it.
One possibility for the sailing ship approach is discovering something equivalent to the parallelogram of force between wind and water which allows sails to propel a sailing ship. Picking up fuel along the way — the ramjet approach — will lose efficiency as the space craft's speed increases relative to the planetary reference. This happens because the fuel must be accelerated to the spaceship's velocity before its energy can be extracted and that will cut the fuel efficiency dramatically. A related issue is drag.
The Chandra X-ray Observatory identified in 1999 more than 200 new point sources. Another space telescope, the Spitzer Space Telescope, found a parallelogram-shaped structure of dust in near infrared images of Centaurus A in 2006. Evidence of gamma emissions with very high energy (more than 100 GeV) was detected by the H.E.S.S-Observatorium in Namibia in 2009. The following year, Centaurus A was identified as a source of cosmic rays of highest energies, after years of observations by Pierre Auger Observatory.
In contrast to pure shear, simple shear describes constant volume strain with rotations. If a cube undergoes simple shearing, the result will be a parallelogram with sides that increase in length and are no longer parallel to the sides of the original cube. The top and bottom of the cube will neither stretch nor shorten. In a simple shear model, a basin is stretched asymmetrically by a large scale detachment fault extending from the upper crust to the lower lithosphere and even asthenosphere.
The Royal Navy had begun the Louisiana Campaign to capture New Orleans. However, to reach New Orleans, the destruction of the small U.S. Navy squadron in the area and the U.S. Army forts and batteries was necessary. Fort St. Philip, an irregular work guarding the Mississippi River, the body of a parallelogram, was one of the said forts. The fort mounted twenty-nine 24-pound cannons, two 32-pound cannons, and two howitzers, an 8-inch and a 5.5-inch.
The present city wall was completed in 1400 as a five kilometers long, crooked parallelogram. Four gate towers were built at its four corner points. The city wall was divided into the actual city wall (also called the high wall), the ground-level and 15-meter-wide kennel in front of it, the kennel wall rising from the moat and the dry moat. A total of about 130 moat and wall towers can be identified on old depictions from the time.
Informally, an affine space is a vector space without a fixed choice of origin. It describes the geometry of points and free vectors in space. As a consequence of the lack of origin, points in affine space cannot be added together as this requires a choice of origin with which to form the parallelogram law for vector addition. However, a vector may be added to a point by placing the initial point of the vector at and then transporting to the terminal point.
This mutual stiffening also permits simple construction: Stewart platform hexapods chains use prismatic joint linear actuators between any-axis universal ball joints. The ball joints are passive: simply free to move, without actuators or brakes; their position is constrained solely by the other chains. Delta robots have base-mounted rotary actuators that move a light, stiff, parallelogram arm. The effector is mounted between the tips of three of these arms and again, it may be mounted with simple ball-joints.
The Dove has solid maple back and sides instead of the solid mahogany used for the Hummingbird, and a longer scale length (25.5" vs 24.75"). These make it a louder, brighter guitar than the Hummingbird. The double parallelogram fingerboard inlays, the two doves on the bridge, and the dove on the pickguard are mother-of-pearl. The original Doves had Gibson's metal tune-o-matic bridge, which seemed like a technological improvement at the time but had negative effects on tone and volume.
Some seat posts are designed with uneven links creating what is not actually a parallelogram so that the arch approximates a straight line when compressed. Various different designs are implemented to tension the seat post, some use elastomers and others use pistons. The size, shape and position of these elastomers and pistons vary by brand and model as well. Some of the elastomers are adjustable by stacking different combinations of elastomer rings to create a specific profile and ramping up of the suspension.
The Verizon Building is located in the Financial District/Tribeca neighborhoods of Lower Manhattan. It occupies an entire city block bounded by West Street to the west, Vesey Street and the World Trade Center to the south, Washington Street to the east, and Barclay Street to the north. Adjacent buildings include 7 World Trade Center to the east and One World Trade Center to the south. The block is parallelogram-shaped, measuring about along West and Washington Streets, along Vesey and Barclay Streets.
According to Martin Gardner, this particular puzzle was invented by a New York City amateur magician, Paul Curry, in 1953. However, the principle of a dissection paradox has been known since the start of the 16th century. The integer dimensions of the parts of the puzzle (2, 3, 5, 8, 13) are successive Fibonacci numbers, which leads to the exact unit area in the thin parallelogram. Many other geometric dissection puzzles are based on a few simple properties of the Fibonacci sequence.
This led to the conclusion that meaningful laws must be homogeneous equations in their various units of measurement, a result which was eventually later formalized in the Buckingham π theorem. Simeon Poisson also treated the same problem of the parallelogram law by Daviet, in his treatise of 1811 and 1833 (vol I, p.39).Martins, p.403 in the Proceedings book containing his article In the second edition of 1833, Poisson explicitly introduces the term dimension instead of the Daviet homogeneity.
Even though the boundary of a neighborhood is a torus, when viewed from inside the link complement, it looks like a sphere. Each link component shows up as infinitely many spheres (of one color) as there are infinitely many light rays from the observer to the link component. The fundamental parallelogram (which is indicated in the picture), tiles both vertically and horizontally and shows how to extend the pattern of spheres infinitely. This pattern, the horoball pattern, is itself a useful invariant.
Designed by Chris Wilkinson Architects, the main depot building is parallelogram shaped, and features a wide by long arched roof that covers 11 maintenance roads. Outside, the depot has 33 stabling roads, with the layout of the 11 hectare site designed to mitigate archaeological impacts to the Stratford Langthorne Abbey. The main depot building was awarded a Civic Trust Award in 1998. As well as the Jubilee line depot, a large training centre for London Underground is located at the site.
In the 1960s and 1970s, Japanese manufacturers introduced their own versions of the derailleur. The Japanese bicycle company, SunTour, notably, introduced the slant parallelogram rear derailleur design in 1964, which is tilted to keep the pulley closer to each cog of the freewheel as it shifts, providing smoother and better shifting than European versions of the time. This version of the derailleur became the standard when SunTour's patent expired in the 1980s, and is still the model for today's designs.
Nagpur is located at the exact centre of the Indian subcontinent, close to the geometric center of the parallelogram connecting the four major metros of India, viz. Chennai, Mumbai, New Delhi and Kolkata. The city has the Zero Mile Stone locating the geographical centre of India, which was used by the British to measure all distances within the Indian subcontinent. The city lies on the Deccan plateau of the Indian subcontinent and has a mean altitude of 310.5 meters above sea level.
Each pier is more or less a parallelogram. Most earlier piers, none of which survive, formed a perfect right angle to the shore, and the curvature of the shore meant that each pier was at a slightly different angle, causing potential for collisions. Their uniform northeast-southwest direction was prescribed by Thomson and Cotterill not only solved that problem but also spared freight trains from needing to make a sharp right angle.Summary for 1201 Alaskan WAY / Parcel ID 7666202485, Seattle Department of Neighborhoods.
The cage is positioned under the desired sprocket by an arm that can swing back and forth under the sprockets. The arm is usually implemented with a parallelogram mechanism to keep the cage properly aligned with the chain as it swings back and forth. The other end of the arm mounts to a pivot point attached to the bicycle frame. The arm pivots about this point to maintain the cage at a nearly constant distance from the different sized sprockets.
An example of a detected feature in an image. Blue indicates the center of the feature, the red ellipse indicates the characteristic scale identified by the feature detector, and the green parallelogram is constructed from the coordinates of the ellipse as per [Lowe 2004]. Feature-based approaches work well for objects which have distinctive features. Thus far, objects which have good edge features or blob features have been successfully recognized; for example detection algorithms, see Harris affine region detector and SIFT, respectively.
Non-uniform scaling (anisotropic scaling, inhomogeneous dilation) is obtained when at least one of the scaling factors is different from the others; a special case is directional scaling or stretching (in one direction). Non-uniform scaling changes the shape of the object; e.g. a square may change into a rectangle, or into a parallelogram if the sides of the square are not parallel to the scaling axes (the angles between lines parallel to the axes are preserved, but not all angles).
Mustacciuoli (also known as mustaccioli or mostaccioli) is a traditional pastry from Naples, usually served at Christmas time. Mustaccioli takes the form of a parallelogram, and consist of a soft, spiced, cake-like interior, covered in chocolate. In recent years, they are many variations of mostaccioli sold in Naples, where the chocolate glaze may be replaced by a white chocolate frosting or icing sugar and candied fruit. Mustacciolis are often sold alongside other Neapolitan sweets including Roccocò, raffiuoli, susamielli, and struffoli at Christmastime.
The principal entrance is a -high archway under the south portico, which contains three highly ornamented wrought iron doors. The smaller, day-to-day entrance is to the east, facing Calverley Street. The Victoria Hall – originally the Great Hall – rises to inside the parallelogram of surrounding rooms and corridors and the enclosing colonnades. It is lined with marble-effect columns with gilt capitals and bases, with painted mottoes around the walls, including "Good Will towards Men", "Trial by Jury", and "Forward".
The William L. Thaxton Jr. House is a large single-story Usonian house, designed by Frank Lloyd Wright in 1954 and built in Houston, Texas in 1955. The Thaxton House is Wright's only residential project in Houston. Thaxton was a successful insurance executive and commissioned Wright to design a work of art that would also be suitable for living and entertaining. This Usonian is one of Wright's smaller designs at 1,800 square feet and is designed as a parallelogram and constructed of concrete block.
If there was a game which featured teams from two of these three markets (involving any combination of the Yankees, Mets, Dodgers, Angels, Cubs or White Sox), that game would be aired on the network. For its first year of coverage in 1996, Fox used the scoring bug on their Major League Baseball telecasts. Within two years, the bug would be expanded to all sports telecasts on Fox and other networks. The first scoring bug was a translucent parallelogram with red borders on the left and right.
Interplane struts were formed by streamlined parallelogram-shaped frames which leaned both outwards and forward because of the different spans and the stagger. The tourer was powered by a water-cooled Hispano-Suiza 8Ab V8 engine with its cylindrical Lamblin radiator mounted below. Its bearers were attached to the forward members of the master-frame. The unusual rear part of the fuselage, a plywood girder structure which deepened but converged in plan progressively rearwards was mounted halfway up the rear master-frame members, near the tie-bar.
The center link transfers the movement from the pitman arm and pitman shaft to the idler arm on the passenger side. The inner tie rods are mounted to the center link and transfer steering motion to the steering arms and outer tie rods. All of the joints which mount these components are constructed of small ball and socket joints to provide the necessary freedom of movement required to maintain control over the vehicle while it is in motion. The most common type of steering is the parallelogram.
The simplest example of a translation surface is obtained by gluing the opposite sides of a parallelogram. It is a flat torus with no singularities. If P is a regular 4g-gon then the translation surface obtained by gluing opposite sides is of genus g with a single singular point, with angle (2g-1)2\pi. If P is obtained by putting side to side a collection of copies of the unit square then any translation surface obtained from P is called a square-tiled surface.
The upper wings were attached to the fuselage at shoulder wing position and the lower ones to the lower fuselage, leaving a gap of about 400 mm (16 in). The stagger placed the trailing edge of the upper wing above the lower wing's leading edge. The upper plane had a longer span and wider chord than the lower one. There were no traditional interplane struts; instead, the wing tips were joined by "curtains", approximately parallelogram-shaped airfoil structures the width of the lower wing.
It is in the shape of a parallelogram, with a dozen bastions on each side. Painted Grey Ware (circa 1100-800 BCE) and Rang-Mahal Ware (1st-3rd century CE) have been found in wells situated along the wall. In the middle of the thirteenth century CE, Sher Shah Suri (Sher Khan), a cousin or nephew of Balban (the Sultan of Delhi), was governor in these parts of the country. He is said to have carried out repairs to the forts of Bhatinda and Bhatner.
The guitar is currently offered only through the Gibson Custom Shop as a special order model. It features two volume and two tone control knobs, a three-way pickup- selector switch, and a three-way neck-selector switch. It has vintage tulip tuners, pearloid split parallelogram inlays, black pickguards and pickup rings, twenty frets per neck (bound with single-ply white binding), and 490 Alnico (R) and 498 Alnico (T) humbucking pickups. The Custom Shop also makes a Don Felder "Hotel California" signature model.
Moving from C to D the arm EM moves through the green parallelogram, with area equal to the area of the rectangle D"DCC". The measuring wheel now moves in the opposite direction, subtracting this reading from the former. The movements along BC and DA are the same but opposite, so they cancel each other with no net effect on the reading of the wheel. The net result is the measuring of the difference of the yellow and green areas, which is the area of ABCD.
In 1669 the Frenchman Gilles Personne de Roberval presented a new kind of balance scale to the French Academy of Sciences. This scale consisted of a pair of vertical columns separated by a pair of equal-length arms and pivoting in the center of each arm from a central vertical column, creating a parallelogram. From the side of each vertical column a peg extended. To the amazement of observers, no matter where Roberval hung two equal weight along the peg, the scale still balanced.
On 6 September 1970 Cork and Wexford faced each other in the first 80-minute All-Ireland final. Wexford took the lead in the fifth minute when a goal resulted from a melee of confusion in the parallelogram. Wexford's lead only lasted five minutes as Cork powered on when Eddie O'Brien flicked the sliotar overhead to the net for Cork's first goal in the eleventh minute. He got his second in the 34th minute when he deflected a Willie Walsh shot to the net.
The rear de Dion transaxle found on the Alfetta and derivatives- GTV, 90 and 75- provided these cars with excellent weight distribution. The handling advantages were noted in contemporary reviews.Cars and Vehicle Magazine, May 1973 The transaxle design, in combination with a Watt's parallelogram linkage, inboard rear brakes and a well-located de Dion rear suspension, resulted in balanced traction and handling. The front suspension design was unusual in that it incorporated independent longitudinal torsion bar springs acting directly onto the lower wishbones and with separate dampers.
Joseph Manigault House, gatehouse The Manigault House is located near the center of the Charleston peninsula, at the corner of Meeting and John Streets. It is a three-story brick structure, set on a raised brick foundation. The main facade has a two- story porch across the center three bays, with elaborate doorways on both floors featuring slender pilasters and sidelight windows. A semicircular stairwell projects from one sidewall, and a bowed porch from the other, giving the house the rough shape of a parallelogram.
In his written work, Yang provided theoretical proof for the proposition that the complements of the parallelograms which are about the diameter of any given parallelogram are equal to one another. This was the same idea expressed in the Greek mathematician Euclid's (fl. 300 BC) forty-third proposition of his first book, only Yang used the case of a rectangle and gnomon. There were also a number of other geometrical problems and theoretical mathematical propositions posed by Yang that were strikingly similar to the Euclidean system.
The nave has the somewhat unusual form of a wide parallelogram 42 feet 8 inches long and 37 feet 2 inches wide, of one span and with no traces of any arcades. The chancel arch is not in the centre of the east wall of the nave, but about five feet nearer to the north side. This has led to the suggestion that when the building was rebuilt in the 1760s, the south wall of the nave was moved further south to enlarge the building.
The resulting tilt is compensated in most CRTs by the tilt and parallelogram adjustments, which impose a small vertical deflection as the beam sweeps across the screen. When properly adjusted, this deflection exactly cancels the downward slope of the scanlines. The horizontal retrace, in turn, slants smoothly downward as the tilt deflection is removed; there's no jump at either end of the retrace. In detail, scanning of CRTs is performed by magnetic deflection, by changing the current in the coils of the deflection yoke.
A conventional cell (which may or may not be primitive) is the smallest unit cell whose axes follow the symmetry axes of the crystal structure. The volume of the conventional cell is always an integer multiple (typically 1, 2, 3, or 4) of the primitive cell volume. The primitive cell is a primitive place. A primitive unit is a section of the tiling (usually a parallelogram or a set of neighboring tiles) that generates the whole tiling using only translations, and is as small as possible.
Magni wanted to produce an "all Italian" machine and turned to Moto Guzzi for a supply of engines. The first Guzzi engined machine was the Magni-Guzzi LeMans 1000, using the engine from the Le Mans 1000. A new frame was designed, which had similarities to the Lino Tonti designed Moto Guzzi item. Magni introduced the "parallelogram" rear suspension, previously used on the 1950 shaft drive MV Agusta 500 cc GP machines, which negated the torque reactions of the shaft drive and made the handing more predictable.
150 Nassau Street is located in the Financial District of Manhattan, just east of New York City Hall and the Civic Center. The building is located on a parallelogram-shaped plot that abuts Nassau Street to the west for and Spruce Street to the north for . The Morse Building is immediately to the south, while a public plaza and 8 Spruce Street is located to the east. The Potter Building and 41 Park Row are located across Nassau Street and Pace University is located across Spruce Street.
In 1976, the Time/Life Corporation sued General Idea for copyright infringement (the corporation held the copyright for white block lettering on a red parallelogram), and demanded that the group cease publication of the magazine. General Idea received a great deal of publicity and sympathetic support. An article appeared in the Village Voice, which included a stern condemnation of the lawsuit by Robert Hughes, Time Magazine's then-art editor. The lawsuit was eventually settled in 1977, with General Idea changing the logo and format of the magazine.
If one of the short (uncrossed) edges of an antiparallelogram linkage is fixed in place, and the remaining linkage moves freely, then the crossing point of the antiparallelogram traces out an ellipse that has the fixed edge's endpoints as its foci. The other moving short edge of the antiparallelogram has as its endpoints the foci of another moving ellipse, formed from the first one by reflection across a tangent line through the crossing point.. For both the parallelogram and antiparallelogram linkages, if one of the long (crossed) edges of the linkage is fixed as a base, the free joints move on equal circles, but in a parallelogram they move in the same direction with equal velocities while in the antiparallelogram they move in opposite directions with unequal velocities.. As James Watt discovered, if an antiparallelogram has its long side fixed in this way it forms a variant of Watt's linkage, and the midpoint of the unfixed long edge will trace out a lemniscate or figure eight curve. For the antiparallelogram formed by the sides and diagonals of a square, it is the lemniscate of Bernoulli., pp. 58–59.
The West Street Building is 23 stories tall. The lower floors occupy the whole parallelogram-shaped lot, while the upper floors contain a "C"-shaped floor plan, with a small "light court" facing east toward the middle of the block.; To comply with the building laws of the 1900s, which required buildings over to be able to withstand of wind pressure, the West Street Building's steel superstructure was braced to protect against wind gusts. The curtain walls on the exterior were reinforced by hollow brick, while portal bracing was used for the steel frame.
A long driveway from the Ophir Road (now Eglinton Road) to the north leads in to the house and loops in front (north) of it, also runs behind (south) of the house to the coach house and stables complex.Bathurst Heritage Study The 16.75ha lot is broadly a parallelogram in shape, its northern boundary facing the (then) Ophir Road. This was the PCO gazetted on 23/3/1984. A driveway running north- south near the eastern boundary approaches the main house and makes a large loop to its north.
The entrance to the system was like a very wide escalator, with broad metal tread plates of a parallelogram shape. After a short distance the tread plates were accelerated to one side, sliding past one another to form progressively into a narrower but faster-moving track which travelled at almost a right angle to the entry section. The passenger was accelerated through a parabolic path to a maximum design speed . The experience was unfamiliar to passengers, who needed to understand how to use the system to be able to do so safely.
Bounding boxes (or bounding volumes) are most often a 2D rectangle or 3D cuboid, but other shapes are possible. A bounding box in a video game is sometimes called a Hitbox. The bounding diamond, the minimum bounding parallelogram, the convex hull, the bounding circle or bounding ball, and the bounding ellipse have all been tried, but bounding boxes remain the most popular due to their simplicity. Bounding boxes are typically used in the early (pruning) stage of collision detection, so that only objects with overlapping bounding boxes need be compared in detail.
Informally, a super-reflexive Banach space X has the following property: given an arbitrary Banach space Y, if all finite- dimensional subspaces of Y have a very similar copy sitting somewhere in X, then Y must be reflexive. By this definition, the space X itself must be reflexive. As an elementary example, every Banach space Y whose two dimensional subspaces are isometric to subspaces of satisfies the parallelogram law, hencesee this characterization of Hilbert space among Banach spaces Y is a Hilbert space, therefore Y is reflexive. So ℓ2 is super- reflexive.
Cervical vertebrae from alt= In conjunction with their long, S-shaped necks, early archosauromorphs had several adaptations of the cervical (neck) vertebrae, and usually the first few dorsal (back) vertebrae as well. The centrum (main body) of each vertebra is parallelogram-shaped, with a front surface typically positioned higher than the rear surface. The transverse processes (rib facets) of these vertebrae extend outwards to a greater extent than in other early reptiles. In many long-necked archosauromorphs, the rib facets are slanted, connecting to cervical ribs that are often long, thin, and dichocephalous (two-headed).
The dorsal part below the fold is only slightly sprinkled with dark scales. There is an irregular series of darker brown spots intervened by pure white dashes on the costal edge from the basal third to the apex. Around the apex and along the base of the dorsal cilia, a thin blackish-brown line is found. Furthermore, there is large, oblique, dark brown spot shaped like a parallelogram on the middle of the dorsal edge, reaching across the light dorsal area to the more densely dusted costal part.
The antiparallelogram has been used as a form of four-bar linkage, in which four rigid beams of fixed length (the four sides of the antiparallelogram) may rotate with respect to each other at joints placed at the four vertices of the antiparallelogram. In this context it is also called a butterfly or bow-tie linkage. As a linkage, it has a point of instability in which it can be converted into a parallelogram and vice versa. Fixing the short edge of an anti­parallelogram linkage causes the crossing point to trace out an ellipse.
He formulated the principle of the parallelogram of forces, but he did not fully recognize its scope. Galileo also was interested by the laws of the pendulum, his first observations of which were as a young man. In 1583, while he was praying in the cathedral at Pisa, his attention was arrested by the motion of the great lamp lighted and left swinging, referencing his own pulse for time keeping. To him the period appeared the same, even after the motion had greatly diminished, discovering the isochronism of the pendulum.
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.
The length of the chapel is , its width as , and its height . The chapel has been described as an "oblong parallelogram....with no tower, aisles, porch, or vestry." The west end of the chapel is said to be the only original part of the building; the east end, with its tessellated floor, was rebuilt after a devastating raid by the Scots in 1321. The tessellated floor underneath the altar is thought to have partially come from a Roman building, as excavations of Roman-period structures in the region have revealed similar designs.
The first logo of Vojvođanska banka was designed in 1962. It contained the two upper-case Latin letters V and B like the geometric shape, where the letter V was shaped as parallelogram and the letter B was shaped as two halves of circle. This logo of the Bank was in use until 1973. From 1973, the Vojvođanska banka logo contained the two lower-case Latin letters v and b, where the letter v was smaller than the letter b and the first letter was placed above the second letter.
Ferdinand Wittenbauer also discovered an easy method to calculate the centroid (centre of mass) of any quadrangle, known as Wittenbauer Theorem or Wittenbauer's Parallelogram. In addition, Wittenbauer is known for his Aufgaben aus der technischen Mechanik, a collection of exercises in technical mechanics including solutions published in three volumes. Co-author was mathematician and engineer Theodor Pöschl (son to Jakob Pöschl Nikola Tesla’s teacher). Finished in 1911, it served as very first and then most prominent set of problems in the fields of mechanics in the German- speaking area for some decades.
Geometric intuition plays an important role in many aspects of Hilbert space theory. Exact analogs of the Pythagorean theorem and parallelogram law hold in a Hilbert space. At a deeper level, perpendicular projection onto a subspace (the analog of "dropping the altitude" of a triangle) plays a significant role in optimization problems and other aspects of the theory. An element of a Hilbert space can be uniquely specified by its coordinates with respect to a set of coordinate axes (an orthonormal basis), in analogy with Cartesian coordinates in the plane.
Moorland to the north-east of the village The south-east boundary of Hebden parish is the River Wharfe, above sea level, and the north- east boundary runs along the Wharfedale-Nidderdale watershed, reaching a height of . The upper section of the eastern boundary is Gate Up Gill, one of the main inflows of Grimwith Reservoir. The parish approximates a parallelogram in shape, averaging under in width and some in length. To the north, the land rises away from Hebden to the summit of Great Whernside, some distant.
The anticline was named after La Tour-Blanche, a small town in the northwestern Dordogne. Yet the centre of the structure is situated farther southeast within the commune of Chapdeuil, hence the names Chapdeuil Anticline or Chapdeuil-La Tour-Blanche Anticline. In plan view the structure has the shape of a nearly rectangular parallelogram with the base lines striking ESE- WNW (N 120) and the sides more or less N-S (reference horizon being the Ligérian/Angoumian boundary). In its long dimension, the anticline measures about 6 km, yet across strike merely 3 km.
Under this winged figure there is a parallelogram diagonally laid and divided by 12 longitudinal lines which interpreted by Calmeyer as wood fuel. Above the tomb the cliff is almost sheer, but from below it is accessible. No attempt has been made to smooth away the rock; and this may indicate that it was a family tomb, used repeatedly. Based on its architecture it can be dated to the Achaemenid period, probably after the reign of Darius I.The tomb has been damaged by fire and graffiti during recent years.
The wings are shortened, the forewings being about and the hindwings . There are a total of fourteen hamuli on the hindwings, all but one located towards the wing tip, with the last just to the base side of the Rs vein. The forewings have a very large parallelogram shaped DC cell and a DC2 cell, which is not seen in wings of Sphecomyrma or Gerontoformica species. Unlike the described Camelomecia females, the male has only eleven antennae segments, and the clypeus lacks denticles, rather a brush of fine setae is present.
Burden and accuracy are usually stated as a combined parameter due to being dependent on each other. :Metering style CTs are designed with smaller cores and VA capacities. This causes metering CTs to saturate at lower secondary voltages saving sensitive connected metering devices from damaging large fault currents in the event of a primary electrical fault. A CT with a rating of 0.3B0.6 would indicate with up to 0.6 ohms of secondary burden the secondary current will be within a 0.3 percent error parallelogram on an accuracy diagram incorporating both phase angle and ratio errors.
This type of bridge has a counterweight suspended in a parallelogram, as well as motors and gears to lift and lower the end of the bridge. In 2006, Skansen Bridge received architectural conservation by the Norwegian Directorate for Cultural Heritage (Riksantikvaren) based upon Skansen Bridge being unique in Norway and only one of a few of its kind left in the world. The conservation includes the entire bridge including construction and technical equipment, the guard cabin and the transformer building. The conservation does not include the railway track, signal equipment or the overhead wires.
In general compactness of the space does not imply completeness of a (G,X)-structure. For example, an affine structure on the torus is complete if and only if the monodromy map has its image inside the translations. But there are many affine tori which do not satisfy this condition, for example any quadrilateral with its opposite sides glued by an affine map yields an affine structure on the torus, which is complete if and only if the quadrilateral is a parallelogram. Interesting examples of complete, noncompact affine manifolds are given by the Margulis spacetimes.
A strain field associated with a displacement is defined, at any point, by the change in length of the tangent vectors representing the speeds of arbitrarily parametrized curves passing through that point. A basic geometric result, due to Fréchet, von Neumann and Jordan, states that, if the lengths of the tangent vectors fulfil the axioms of a norm and the parallelogram law, then the length of a vector is the square root of the value of the quadratic form associated, by the polarization formula, with a positive definite bilinear map called the metric tensor.
In Euclidean geometry, a kite is a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other. In contrast, a parallelogram also has two pairs of equal-length sides, but they are opposite to each other rather than adjacent. Kite quadrilaterals are named for the wind-blown, flying kites, which often have this shape and which are in turn named for a bird. Kites are also known as deltoids, but the word "deltoid" may also refer to a deltoid curve, an unrelated geometric object.
During the field trials, the 20-ton tank proved to be under- powered. The weight of the initial prototype and its low speed performance did not impress the Imperial Japanese Army General Staff Office, and a new requirement was issued for a lighter tank, with a nominal weight. The new design was modeled after a Vickers Medium Mark C tank, which had been purchased by the Japanese Army in March 1927. The Chi-I had a complex parallelogram suspension system with two pairs of road bogie wheels per leaf spring arrangement.
Ground plan of Abbotsford. Study room The general ground-plan is a parallelogram, with irregular outlines, one side overlooking the Tweed; and the style is mainly the Scottish Baronial. With his architects William Atkinson and Edward Blore Scott was a pioneer of the Scottish Baronial style of architecture: the house is recognized as a highly influential creation with themes from Abbotsford being reflected across many buildings in the Scottish Borders and beyond. The manor as a whole appears as a "castle-in- miniature", with small towers and imitation battlements decorating the house and garden walls.
The muscle architecture of pennate muscles, such as the human quadriceps, is highly plastic and strongly influences contractile properties. Changes to pennate muscle architectural properties, such as pennation angle and thereby the PCSA, can alter the muscle’s force producing capabilities as well as the AGR at which the muscle operates. Parallelogram models predict that total PCSA of bipennate muscles increases in proportion to sin(θpennation) while total force exerted on the associated aponeurosis decreases with cos(θpennation). This theorizes that pennate muscle force generation increases until a 45 degree pennation angle is achieved.
Note the grid point where the red and blue triangles in the lower image meet (5 squares to the right and two units up from the lower left corner of the combined figure), and compare it to the same point on the other figure; the edge is slightly under the mark in the upper image, but goes through it in the lower. Overlaying the hypotenuses from both figures results in a very thin parallelogram (represented with the four red dots) with an area of exactly one grid square, so the "missing" area.
The first wave of Hummingbirds came with a solid Sitka spruce top and solid mahogany back. The sides are mahogany, but not all of them are solid, many are laminated. They have adjustable rosewood or ceramic saddles, three-ply maple bridge plates, single X-bracing, engraved hummingbird-butterfly trumpet-flower pickguards with two points on the upper treble bout and one point level with the bridge, as well as bound fretboards with double parallelogram inlays, a crown peghead inlay on the headstock, golden green button tulip tuners, and a cherryburst (a.k.a. cherry sunburst) finish.
An electric garage-door opener operates on the center track A typical version of an overhead garage door used in the past would have been built as a one-piece panel. The panel was mounted on each side with unequal parallelogram style hinge lifting mechanism. Newer versions of overhead garage doors are now generally built from several panels hinged together that roll along a system of tracks guided by rollers. The weight of the door may be or more, but is balanced by either a torsion spring system or a pair of extension springs.
Ackermann steering linkage Idler arm for a heavy-duty truck On an automobile or truck with a conventional parallelogram steering linkage, the idler arm or idler arm assembly is a pivoting support for the steering linkage. The idler arm supports the end of the center link on the passenger's side of the vehicle. The idler arm bolts to the vehicle's frame or subframe. Generally, an idler arm is attached between the opposite side of the center link from the Pitman arm and the vehicle's frame to hold the center link at the proper height.
The chapel of Carburton that is dedicated to Saint Giles is a small edifice that is said to be stood on land liable to flood. There has been no mention of the church in the Domesday Book as the place always seems to have been quite small. It is a simple parallelogram that is 50 ft long and about 15 ft wide. It is made up of a chancel and a nave, as well as having a porch to the south-west and a small vestry to the north-east.
The Upper Cox Brook Covered Bridge stands west of the village of Northfield Falls, crossing Cox Brook, a tributary of the Dog River. It is the westernmost of three covered bridges on Cox Brook Road; the other two are the Northfield Falls Covered Bridge (crossing the river), and the Lower Cox Brook Covered Bridge. The bridge is of Queen post truss design, its two trusses in length, and resting on abutments either faced or rebuilt in concrete. The trusses are set at an offset, skewed to form a parallelogram.
They had destroyed the houses, burned the gardens, uprooted all the trees and demolished the ramparts of the city fortress. Voulgaris specifically proposed to erect the modern city on the seaside, which was then a freer and more extensive area. The city, with a geometric composition, took the form of a large parallelogram bordering the coastal area and of a second ending at the periphery of the old town. Seventeen vertical and wide uphill streets intersected, at right angles, eight other horizontal streets, thus dividing the city into a hundred large blocks of buildings.
More general is scaling with a separate scale factor for each axis direction. Non-uniform scaling (anisotropic scaling) is obtained when at least one of the scaling factors is different from the others; a special case is directional scaling or stretching (in one direction). Non-uniform scaling changes the shape of the object; e.g. a square may change into a rectangle, or into a parallelogram if the sides of the square are not parallel to the scaling axes (the angles between lines parallel to the axes are preserved, but not all angles).
The design was extensively copied by other companies, usually in simplified form, and is still in use. Some derivatives use a heavy balance weight instead of the springs. The most common version replaces the arm linkages with two independent parallelogram linkages, with a pair of light tension springs on each half of the arm. The arm has been employed in other devices where it is necessary to hold an object stationary at a convenient point in space, notably the copy holder for typists and in some applications, the computer display screen.
"Parallelogram" and "Little Nemo in Nightland" are some of his most notable "compositions" from this release. In addition to his songwriting, producing, and MIDI programming activities for the Grateful Dead, Bralove is known for his performing and designing with the Grateful Dead and the avant-garde "Drums and Space" segments of their live shows with the Rhythm Devils. Bralove was also a member and producer of the Psychedelic Keyboard Trio, along with former Grateful Dead keyboardist Tom Constanten and Vince Welnick, former keyboardist for the Grateful Dead and the Tubes.
Thus each snapped-off piece is roughly a parallelogram, with each long edge being a breaking edge, and one or both of the short ends being a sharpened edge. Inexpensive stamped steel and aluminum box cutter with disposable razor blade. Another utility knife often used for cutting open boxes consists of a simple sleeve around a rectangular handle into which single-edge utility blades can be inserted. The sleeve slides up and down on the handle, holding the blade in place during use and covering the blade when not in use.
The wing was internally braced with diagonal steel tubes and fabric-covered. Externally, it was braced on each side with a steel tube strut from the lower fuselage longeron to the main spar at about 40% span. The fuselage was a steel tube structure which from the wing rearwards had four longerons forming a parallelogram section, deeper than wide. There was additional cross-bracing under the wing and a low, shelf-like forward projection to carry the wooden-framed open cockpit, placed just ahead of the wing leading edge, and the nose.
The School Addition Historic District encompasses a middle-class residential area of Batesville, Arkansas that typifies its growth between about 1850 and 1950. It is located between Main Street and Poke Bayou, along two blocks each of Rock and Water Streets (offset to give the district the shape of a parallelogram), and the intervening blocks of 7th and 8th Streets. Houses in this area are generally of a modest scale, built for tradesmen and craftsmen. They come in a variety of styles, including the traditional I-house, American Craftsman-style bungalows, and ranches.
130 Cedar Street (left) and 90 West Street (right) as seen from the National September 11 Memorial to the north 90 West Street is located on a plot facing West Street to the west, Cedar Street and the World Trade Center to the north, and Albany Street to the south. The lot is roughly parallelogram-shaped. The building shares its block with 130 Cedar Street, a 19-story hotel. The building carries the address numbers 87–95 West Street, inclusive, as well as odd address numbers 21–25 Albany Street and even address numbers 136–140 Cedar Street.
The portal ends and the interiors of the portals are also finished in vertical board siding. Although the trusses are set to form a rectangle, the portals are slightly skewed, giving the bridge a parallelogram shape on the outside. with The bridge was built in 1902, and is one of only two documented early 20th-century bridges in the state; the other is the Kingsbury Covered Bridge in nearby Randolph, built in 1904. The bridge is one of five in Tunbridge, which, when combined with one in Chelsea, form a remarkably dense concentration of covered bridges across a single waterway in the state.
Plan of Allington Castle in 1906 Allington Castle takes the form of an irregular parallelogram with a curtain wall incorporating six round towers of various sizes. A gatehouse, incorporating the remains of the original manor house from which the castle developed, stands on the north-west side. The largest and most significant of the towers, the four-storeyed Solomon's Tower, projects from the south-west side of the curtain wall. Just to its north, adjoining the west curtain wall, is the Penchester Lodgings, one of two surviving ranges of early buildings, which may incorporate remains of the earlier manor house.
The single-stemmed (not clumping) plant grows to 5-6m in the park, and is noted for its big parallelogram-shaped leaf, with a wrinkled surface and wavy border. Subspecies bousigonii has rachis bracts that are strictly tubular and for the most part intact, not splitting, and the first order branches are inserted at the mouth of the bracts. The smitinandii subspecies is "one of the most attractive of all Thai rattans ... glossy undulate diamond-shaped leaflets and its neat low habit give it considerable horticultural potential[, a]mong Thai species it is very distinctive." John Dransfield.
The New York World Building was at 53–63 Park Row, at the northeast corner with Frankfort Street, in the Civic Center of Manhattan. The building initially occupied a roughly parallelogram-shaped land lot with frontage of on Park Row to the northwest and on Frankfort Street to the south. It abutted the Brooklyn Bridge to the north and other buildings to the east; the lot originally had a cut-out on the northeastern corner so that the Brooklyn Bridge side was shorter than the Frankfort Street side. Immediately to the south of the site was the New York Tribune Building.
The Stockade District is parallelogram-shaped, with its boundaries defined as the rear property lines of lots on the far side of North Front Street on the north, Green Street on the west, Main Street on the south and Clinton Avenue on the east. Crown Street is entirely within the district, as are the intersecting segments of Fair, John and Wall streets. It also extends slightly along Frog Alley to take in the Lowe-Bogardus ruin and an interpretive exhibit with some of the original stockade at Frog Alley on the northwest corner. The total area is .
Stephenson's bridge A close-up of the technique 1830 also saw the grand opening of the skew bridge in Rainhill over the Liverpool and Manchester Railway. The bridge was the first to cross any railway at an angle. It required the structure to be constructed as two flat planes (overlapping in this case by ) between which the stonework forms a parallelogram shape when viewed from above. It has the effect of flattening the arch and the solution is to lay the bricks forming the arch at an angle to the abutments (the piers on which the arches rest).
Benzene, the model π system, has no permanent dipole moment, as the contributions of the weakly polar carbon–hydrogen bonds cancel due to molecular symmetry. However, the electron-rich π system above and below the benzene ring hosts a partial negative charge. A counterbalancing positive charge is associated with the plane of the benzene atoms, resulting in an electric quadrupole (a pair of dipoles, aligned like a parallelogram so there is no net molecular dipole moment). The negatively charged region of the quadrupole can then interact favorably with positively charged species; a particularly strong effect is observed with cations of high charge density.
Behind the seat is a mild aluminum grab-bar that corrals the taillight above the fender and flows halfway down the rear cowl/fender, the cowl/fender is painted to match the other bodywork. The side covers are an uneven parallelogram shape to match the frame and seat's bottom edge. The right side cover also emulates the rectifier-regulator found on the left side, the side covers are typically chrome with a full decal over the raised center section. The exhaust was a completely chrome 2 into 2 system utilizing a resonator/power-chamber above the centerstand.
The caribou, standing atop a cairn of Newfoundland granite, appears to roar in the direction of the enemy the Newfoundlanders faced during the battle. The Masnières Memorial is situated on the west side of the D644 road, at the north end of the village of Masnières. The Caribou is surrounded by a small park, roughly in the shape of a parallelogram. The Monument itself is situated in the centre of the park; at the cairn's base is a circular garden and, surrounding that, is a level lawn of grass with several maple trees at points around the three sides away from the road.
The outer plywood sheet of the PFP sandwich was then wrapped continuously around and glued to the inner layers, leaving no gaps. Final external shaping reduced the waviness to 50 μm. Before this outer layer was attached, the area of it corresponding to the last 30% of chord, where it formed the whole skin thicknees, was weakened by cuts through its inner plies, making it flexible enough to warp when driven by internal parallelogram frames opened and closed by lateral control rods. The edges could be warped differentially to act as ailerons or together to change camber.
Utilising its three-wheel mechanism, the MP3 can be stopped and parked, without using a traditional kickstand or centre stand, and can be parked on irregular or side-sloping ground. The front suspension is similar to the single-sided trailing arm of Vespa-style suspensions, linked by an alloy parallelogram and a central steering arm. When moving at slow speeds or stopped, the rider maintains balance by maintaining forward motion or placing feet on the ground. The front suspension locks or unlocks using a switch, which is located just below the throttle on the right handlebar.
The former Maple Avenue substation of the Hartford Electric Light Company stands in southern Hartford's Barry Square area, on the east side of Maple Avenue between Adelaide and Barker Streets. It is a single- story brick building, shaped in a rough parallelogram to accommodate Maple Avenue's diagonal traversal of the city street grid. Its walls are buff brick laid in common bond, and it has a five-bay front facade, articulated by projecting brick pilasters with papyrus-leaf capitals. A double-leaf door in the southernmost bay provides entry to the building, sheltered by a metal hip- roofed hood.
The nature of the unit cell can be determined by inspecting the "auxiliary rectangle" (generally a parallelogram), which is a rectangle formed by the origin (0,0) at one corner, and (K,K') as the diagonally opposite corner. As in the diagram, the four corners of the auxiliary rectangle are named s, c, d, and n, going counter-clockwise from the origin. The function pq(u,m) will have a zero at the "p" corner and a pole at the "q" corner. The twelve functions correspond to the twelve ways of arranging these poles and zeroes in the corners of the rectangle.
The sums of the areas of opposing triangles are equal, that is Area(BCL) + Area(DAL) = Area(LAB) + Area(DLC) Anne's theorem, named after the French mathematician Pierre-Leon Anne (1806–1850), is a statement from Euclidean geometry, which describes an equality of certain areas within a convex quadrilateral. Specifically, it states: :Let ABCD be a convex quadrilateral with diagonals AC and BD, that is not a parallelogram. Furthermore let E and F be the midpoints of the diagonals and L be an arbitrary point in the interior of ABCD. L forms four triangles with the edges of ABCD.
The configuration space of 2 not necessarily distinct points on the circle is the orbifold quotient of the 2-torus, T2/S2, which is the Möbius strip. The Tonnetz is an example of a torus in music theory. The Tonnetz is only truly a torus if enharmonic equivalence is assumed, so that the segment of the right edge of the repeated parallelogram is identified with the segment of the left edge. As the n-torus is the n-fold product of the circle, the n-torus is the configuration space of n ordered, not necessarily distinct points on the circle.
Burden and accuracy are usually stated as a combined parameter due to being dependent on each other. :Metering style PTs are designed with smaller cores and VA capacities than power transformers. This causes metering PTs to saturate at lower secondary voltage outputs saving sensitive connected metering devices from damaging large voltage spikes found in grid disturbances. A small PT (see nameplate in photo) with a rating of 0.3W, 0.6X would indicate with up to W load (12.5 watts ) of secondary burden the secondary current will be within a 0.3 percent error parallelogram on an accuracy diagram incorporating both phase angle and ratio errors.
In a parallelogram ABCD with a point P on the diagonal AC the parallel to AD through P intersects the side CD in G and the side AB in H. Similarly the parallel to the side AB through P intersects the side AD in I and the side BC in F. The theorem of the gnomon now states, that the parallelograms HBFP and IPGD have equal areas.Lorenz Halbeisen, Norbert Hungerbühler, Juan Läuchli: Mit harmonischen Verhältnissen zu Kegelschnitten: Perlen der klassischen Geometrie. Springer 2016, , pp. 190-191William J. Hazard: Generalizations of the Theorem of Pythagoras and Euclid's Theorem of the Gnomon.
The melody for this song also appears in part in The Lemonheads' song "Purple Parallelogram", which was co-written between Noel Gallagher and Evan Dando . The song's chorus is frequently played as background music for the Fox Sports English Premier League adverts in Australia. "Roll With It" is regularly played after matches at Celtic Park. "Roll With It" featured at the end of the Red Nose Day 2015 sketch titled "Who's Got What It Takes to Be a National Treasure", which featured a cameo appearance from Liam Gallagher who was made a National Treasure by Stephen Fry, Miranda Hart and Sheridan Smith.
Geometric equipollence is also used on the sphere: :To appreciate Hamilton's method, let us first recall the much simpler case of the Abelian group of translations in Euclidean three- dimensional space. Each translation is representable as a vector in space, only the direction and magnitude being significant, and the location irrelevant. The composition of two translations is given by the head-to-tail parallelogram rule of vector addition; and taking the inverse amounts to reversing direction. In Hamilton's theory of turns, we have a generalization of such a picture from the Abelian translation group to the non-Abelian SU(2).
The front seat was under the wing but the rear one was behind the trailing edge, which had a rectangular cut-out for better upward vision. Alternatively, the seats could be arranged tightly side- by-side, though with slight stagger, which allowed single controls to be shared and eased communication. The RB.1's empennage was conventional, with a broad-chord, rectangular plan tailplane mounted on top of the fuselage and carrying elevators with a large central cut-out for rudder movement. Its triangular fin mounted a parallelogram profile rudder which reached down to the keel.
But, by the symmetries of its construction, the flexing motions of these two open pyramids both move the equator along which they were cut in the same way. Therefore, they can be glued back together into a single flexing motion of the whole octahedron. The property of having opposite sides of equal length is true of the rectangle, parallelogram, and antiparallelogram, and it is possible to construct Bricard octahedra having any of those flat shapes as their equators. However, the equator of a Bricard octahedron is not required to lie in a plane; instead, it can be a skew quadrilateral.
The Rackleff Building is located in Portland's Old Port area, on the north side of Middle Street, west of Franklin. It is flanked on the left side by the Woodman Building, and is separated on the right from the Thompson Block by Church Street, a narrow side street. The building is three stories in height and roughly a parallelogram in shape, with a rounded section at the sharply angled corner with Church Street. The ground floor has a cast iron facade that is essentially the same as that of the Woodman building, but about one foot shorter.
Lincoln Park is located near the geographic center of peninsular Portland, at the southern corner of Congress and Franklin Streets. It is shaped roughly like a parallelogram, and is a relatively flat open grassy area, dotted with trees. A network of walking paths radiate away from a fountain located near the center of the park, and there are internal park walkways adjacent to Congress and Federal Streets. (The fountain was originally at the park's center, but its eastern boundary was reduced in order to widen Franklin Street, a major city artery.) The park is encircled by iron fencing.
Orthogonal diameters of a circle with a square of tangents, midpoints of parallel chords and an affine image, which is an ellipse with conjugate diameters, a parallelogram of tangents and midpoints of chords. A circle has the following property: : The midpoints of parallel chords lie on a diameter. An affine transformation preserves parallelism and midpoints of line segments, so this property is true for any ellipse. (Note that the parallel chords and the diameter are no longer orthogonal.) ; Definition: Two diameters d_1,\, d_2 of an ellipse are conjugate if the midpoints of chords parallel to d_1 lie on d_2\ .
Fresnel's zone plates have rings with equally spaced squared distances to the center The square function is related to distance through the Pythagorean theorem and its generalization, the parallelogram law. Euclidean distance is not a smooth function: the three-dimensional graph of distance from a fixed point forms a cone, with a non-smooth point at the tip of the cone. However, the square of the distance (denoted or ), which has a paraboloid as its graph, is a smooth and analytic function. The dot product of a Euclidean vector with itself is equal to the square of its length: .
Women had been allowed to take the Tripos since 1880, after Charlotte Angas Scott was unofficially ranked as eighth wrangler. When the women's list was announced, Fawcett was described as "above the senior wrangler". No woman was officially awarded the first position until Ruth Hendry in 1992. An anonymous poem written in 1890 paying tribute to Fawcett's great achievement climaxes with the following two stanzas, mentioning the other respected mathematicians Arthur Cayley and George Salmon: > Curve and angle let her con and Parallelopipedon and Parallelogram Few can > equal, none can beat her At eliminating theta By the river Cam.
The firm Glasflügel () was founded by Eugen Hänle in 1962 and was located in Schlattstall, south of Kirchheim unter Teck. It was the first firm to manufacture a glass-fibre sailplane in large numbers. It was also responsible for a large number of innovations in sailplane design and technology: quick assembly systems for wings and tailplane, automatic control connections, trailing edge airbrake-flap combinations, hinged instrument panels, the parallelogram control stick and automatic trimming are some innovations introduced by Glasflügel and later adopted by other manufacturers. Some of these are standard features in nearly all gliders produced today.
Reconstructed skeleton in Japan The neck consisted of nine cervical vertebrae, which would have formed an S-shaped curve, as indicated by the shape of the vertebral bodies in the side view of the skeleton. The vertebral bodies of the anterior cervical vertebrae are shaped like a parallelogram, those of the middle are rectangular and those of the posterior show a trapezoid shape. The trunk was short, consisting of 12 dorsal and 6 fused sacral vertebrae. The tail was long compared to the body; although incompletely known, it probably consisted of 34 to 37 caudal vertebrae.
1928 saw the introduction of the "Super Champion Gear" (or "Osgear") from the company founded by champion cyclist Oscar Egg, as well as the Vittoria Margherita; both employed chainstay mounted 'paddles' and single lever chain tensioners mounted near or on the downtube. However, these systems, along with the rod-operated Campagnolo Cambio Corsa were eventually superseded by parallelogram derailleurs. In 1937, the derailleur system was introduced to the Tour de France, allowing riders to change gears without having to remove wheels. Previously, riders would have to dismount in order to change their wheel from downhill to uphill mode.
Hitchcock at Coolidge Corner Theatre in 2010 In 2006 Olé! Tarantula was released with the Venus 3, a band which consisted of longtime friends and collaborators R.E.M.'s Peter Buck and Young Fresh Fellows' frontman Scott McCaughey, as well as Ministry's Bill Rieflin (by then also R.E.M.'s full-time drummer). The song "'Cause It's Love (Saint Parallelogram)" was written with Andy Partridge of XTC. In 2007, he was the subject of a documentary Robyn Hitchcock: Sex, Food, Death... and Insects directed by John Edginton, shown on the U.S. Sundance Channel and in the UK on BBC Four (and later released on DVD).
A well-known formula due to the mathematician Édouard Lucas characterizes the structure of every 3 × 3 magic square of numbers."Alphamagic Squares", thinkquest.org:Magic of Mathematics Sallows, already the author of original work in this area,"New advances with 4 × 4 magic squares" by Lee Sallows had long speculated that the Lucas formula might contain hidden potential.Sallows, pp 3 and 91 This surmise was confirmed in 1997 when he published a short paper that examined squares using complex numbers, a ploy leading to a new theorem that correlated every 3 × 3 magic square with a unique parallelogram on the complex plane.
First, the fort's military engineers modified the usual rectangular plan to suit the available site: it is distorted into a lozenge or parallelogram; the internal features of the fort are similarly distorted. Six barracks were however fitted in behind the headquarters building (principia), and four in front of it, in a limited area of . Second, the wall is surrounded by four steep defensive ditches and banks around the hill spur, and seven such ramparts across the uphill side of the spur. These constitute the most complex defensive earthworks of any known Roman fort, with multiple banks and ditches outside the usual stone ramparts.
An opened Toshie's Jewel'. Each individual unit is folded from a square sheet of paper, of which only one face is visible in the finished module; many ornamented variants of the plain Sonobe unit that expose both sides of the paper have been designed. The Sonobe unit has the shape of a parallelogram with 45 and 135 degrees angles, divided by creases into two diagonal tabs at the ends and two corresponding pockets within the inscribed center square. The system can build a wide range of three-dimensional geometric forms by docking these tabs into the pockets of adjacent units.
From the point of view of topology, the seminormed vector space that we started with has a lot of extra structure; for example, it is a vector space, and it has a seminorm, and these define a pseudometric and a uniform structure that are compatible with the topology. Also, there are several properties of these structures; for example, the seminorm satisfies the parallelogram identity and the uniform structure is complete. The space is not T0 since any two functions in L2(R) that are equal almost everywhere are indistinguishable with this topology. When we form the Kolmogorov quotient, the actual L2(R), these structures and properties are preserved.
This low one-story home is built of Wisconsin limestone, redwood board and batten, and glass. It is one of Wright's diamond module homes, a form he used in the Patrick and Margaret Kinney House, the Richard Smith House and a number of other homes he designed in the late 1940s and early 1950s. In this design, all the angles are either 60°or 120°, forming equilateral parallelogram modules having sides. It was originally built with two wings set at 120° angles which gave the house a V-shaped plan with a living room wing, a bedroom wing, and a central core that contained the fireplace mass, kitchen, and utilities.
A parallelogram steering linkage is called such because like its name sake the two sides of the linkage run parallel to each other and are equal in distance. This type of steering linkage uses four tie rods, one inner and one outer on each side (left and right), a center link (which runs between the tie rods), an idler arm on the passenger side, and a pitman arm on the driver side. The pitman arm attaches to the steering gear output shaft which is also commonly called the pitman shaft. The pitman arm attaches to the center link and is moved by turning the steering wheel.
Camp C () is situated to the north-east of camps A and B on the east side of Dere Street and astride the modern road from Pennymuir to Hownam.Towford; Pennymuir, Camp C; Dere Street, RCAHMS, accessed 8 May 2014 It has been partially obliterated by drainage and a plantation. The camp is a parallelogram in shape, and measures 280 metres from northwest to southeast by 185 metres, and encloses 5.1 hectares. The only visible part is the west side, south of the Pennymuir road, where it is traceable for 50 metres as a slight turf bank, some 2 metres wide and 20 centimetres high.
Community Christian Church, designed by Frank Lloyd Wright and located adjacent to the Country Club Plaza This Frank Lloyd Wright building sits across from the Country Club Plaza's main shopping district, located on Main at East 46th Street. In April 1940, Community Christian Church came to Wright and asked him to design a new building for them after a fire had destroyed their last church. Wright based his design on a parallelogram including some features previously conceived for his last building for Johnson Wax Company, along with one additional unique feature: a spire of light. Due to high building costs, the scale of the church was reduced during construction.
The new groupset made use of a 10-42 cassette and a patented single front chainring that made use of both narrow and specially shaped wide teeth to retain the chain without a chain guide. The rear derailleur for the groupset uses a parallelogram that moves only laterally, known as X-Horizon, which is intended to improve shifting precision and chain retention. SRAM Eagle XX1 Drivetrain By 2014, this same technology was adapted for use on cyclocross bikes with the introduction of SRAM Force CX1. The group was expanded in 2015 to use chainrings (up to 54-teeth) for other applications such as TT/Tri, road, and fitness bikes.
The Broad Art Museum at Michigan State University in East Lansing, Michigan, Hadid's second project in the United States, has a space of 4,274 square metres, dedicated to contemporary art and modern art and an historical collection. The parallelogram-shaped building leans sharply and seems about to tip over. Hadid wrote that she designed the building so that its sloping pleated stainless steel facades would reflect the surrounding neighbourhood from different angles; the building continually changes colour depending upon the weather, the time of day and the angle of the sun. As Hadid commented, the building "awakens curiosity without ever truly revealing its contents".
If the two sums of areas of opposite triangles are equal ( Area(BCL) + Area(DAL) = Area(LAB) + Area(DLC) ), then the point L is located on the Newton line, that is the line which connects E and F. For a parallelogram the Newton line does not exist since both midpoints of the diagonals coincide with point of intersection of the diagonals. Moreover the area identity of the theorem holds in this case for any inner point of the quadrilateral. The converse of Anne's theorem is true as well, that is for any point on the Newton line which is an inner point of the quadrilateral, the area identity holds.
MVPSI's Leyland Leopard with Supreme IV bodywork The design received a facelift in 1978, with the first examples of the new Supreme IV entering service towards the end of that year. The windscreen shape was altered again, this time to have a flatter top, and the ridged area above it was done away with. The grille and headlight area underwent a complete revision, with twin rectangular headlights flanking a grille of three chunky slats (although some vehicles had an optional rectangular chrome grille). The kink in the side trim was replaced by a parallelogram-shaped link between straight sections, and the window in the door was deeper.
An early surviving reference to the work is by Patriarch Photios I of Constantinople in the 9th century AD. Photius condemns the style and syntax of the text as well as the honesty of the author. More recent authors tend to agree with Photius on the stylistic points, but do find the author generally reliable for geographical and historical references. Edward Gibbon, for example, said "the nonsense of the Monk was, nevertheless, mingled with the practical knowledge of the traveller" and used it in writing The History of the Decline and Fall of the Roman Empire.Cosmas Indicopleustes, Christian Topography (1897) Introduction The world according to the book is a parallelogram.
Bases are commonly used (together with heights) to calculate the areas and volumes of figures. In speaking about these processes, the measure (length or area) of a figure's base is often referred to as its "base." By this usage, the area of a parallelogram or the volume of a prism or cylinder can be calculated by multiplying its "base" by its height; likewise, the areas of triangles and the volumes of cones and pyramids are fractions of the products of their bases and heights. Some figures have two parallel bases (such as trapezoids and frustums), both of which are used to calculate the extent of the figures.
Seen from the northwest corner, near Hudson and Worth Streets 60 Hudson Street contains numerous setbacks on its exterior. Though setbacks in New York City skyscrapers were mandated by the 1916 Zoning Resolution in order to allow light and air to reach the streets below, they later became a defining feature of the Art Deco style. 60 Hudson Street's massing mostly uses rectangular shapes in spite of its trapezoid-shaped lot. This may have been a response to architecture critic Lewis Mumford's previous criticism of the Barclay–Vesey Building's shape; that building had been shaped around its parallelogram-shaped lot, which Mumford had described as an "annoying defect".
Community Christian Church was designed by Frank Lloyd Wright and sits across from the Country Club Plaza's main shopping district on Main Street at East 46th Street in Kansas City, Missouri. In April 1940, members of the church congregation contracted Wright and asked him to design a new building to replace their previous church which had been destroyed in a fire. Wright based his design on a parallelogram including some features previously conceived for his last building for Johnson Wax Company, along with one additional unique feature: a spire of light. Due to high building costs, the scale of the church was reduced during construction.
The Krumm drains 30.0 km² at the middle Albtrauf southwest of the Fils. Its catchment area has roughly the shape of a parallelogram with a longer diagonal from northeast to southwest of about 10 km, perpendicular to it the maximum width reaches a little over 5 km. Its northwest corner lies on the 684.1 m tall Hohenstaufen, the northeastern one on Rechberg at an elevation of 707.9 m above sea level, the southeastern one at an unnamed, 564.6 m tall peak east of the Salacher Kapfhöfe, the southwestern one at the mouth (below 330 m ). The highest point is at the top of the Rechberg.
Jenga Xtreme used parallelogram-shaped blocks that could create some interesting leaning towers. Casino Jenga: Las Vegas Edition employed roulette-style game play, featuring a felt game board, betting chips, and additional rules. In addition, there have been a number of collector edition Jenga games, featuring the colors and logos of the Boston Red Sox, Las Vegas Raiders, New York Yankees, and John Deere, among others. Fortnite Jenga, Hello Kitty Jenga, Transformers Jenga, Tarzan Jenga, Tim Burton's The Nightmare Before Christmas Jenga, Donkey Kong Jenga, Bob's Burgers Jenga, National Parks Jenga, Jenga Ocean, The Walking Dead Jenga, and Super Mario Jenga are some of the licensed variations of Jenga.
The 18th century plaza vieja (old plaza) predates the 19th century plaza nueva. The old plaza of El Pueblo de Nuestra Señora, La Reina de Los Angeles (the town of our Lady, the Queen of the Angels) as decreed by Gov. Felipe de Neve in his "Instruccion para La Fundaccion de Los Angeles" (26 August 1781), was a parallelogram one hundred varas in length by seventy-five in breadth. It was laid out with its corners facing the four winds or cardinal points of the compass, and with its streets running at right angles to each of its four sides, so that no street would be swept by the wind.
Taken from [Rothganger et al. 2004]. Next, given a number of camera views of the object (24 in the paper), the method constructs a 3D model for the object, containing the 3D spatial position and orientation of each feature. Because the number of views of the object is large, typically each feature is present in several adjacent views. The center points of such matching features correspond, and detected features are aligned along the dominant gradient direction, so the points at (1, 0) in the local coordinate system of the feature parallelogram also correspond, as do the points (0, 1) in the parallelogram's local coordinates.
AK-5 in the Alps near Timmersdorf The forward fuselage of the glider was taken from the Glasflügel 604 and the wings were built to the design of the Streifeneder-Hansen Falcon glider, an experimental prototype designed and built by Hansjörg Streifeneder. The cockpit interior was newly designed including a self-designed and built flight director / variometer system and parallelogram control input system similar to Glasflügel practice. The experience gained while building the new winglets for the AK-8 glider will be used to improve the performance of the AK-5. It is planned to build extensions to the existing wings and to attach winglets.
Designed by architect Francis Petre, with an axis of east-west rather than the west-east of its predecessor, Sacred Heart was built on a classical basilican plan. However, its portico of Ionic columns of Oamaru stone, whose pedestals rest on elongated plinths, and a high pediment closely reflect those of a Roman or Greek temple, and, in that respect, its most obvious model is the Maison Carrée, Nimes, which has full-length, Corinthian, columns. The building is within the classical proportions and forms a parallelogram (accommodating a clerestory with rows of arch-topped windows) of about 42 metres by 19 metres by a height of 18 metres.
Along with the Osaka Army Arsenal, Sagami Army Arsenal was also assigned to oversee the design and manufacture of assorted types of armored vehicles and tanks. The Chi-I had a complex parallelogram suspension system with two pairs of road bogie wheels per leaf spring arrangement. Hara designed a bell crank scissors suspension that paired the bogie wheels and connected them to a coil spring mounted horizontally outside the hull. This suspension became standard on the majority of the subsequently designed Japanese tanks and can be seen on the Type 95 Ha- Go light tank and Type 97 Chi-Ha medium tank, as examples.
Seasat carried five major instruments designed to return the maximum information from ocean surfaces: # Radar altimeter to measure spacecraft height above the ocean surface # Microwave scatterometer to measure wind speed and direction # Scanning multichannel microwave radiometer to measure sea surface temperature # Visible and infrared radiometer to identify cloud, land and water features # Synthetic aperture radar (SAR) L-band, HH polarization, fixed look angle to monitor the global surface wave field and polar sea ice conditions {the antenna is the light parallelogram in the picture}. The SAR support structure was designed and manufactured by Northrop Grumman Astro Aerospace in Carpinteria, California. The structure deployed on orbit. Many later remote sensing missions benefited from Seasat's legacy.
Then BGCL is a parallelogram, the two triangles BGL and CLG into which it may be subdivided are both similar to ABC, G is the midpoint of AL, and the Euler line of the triangle is the perpendicular bisector of AL. When generating a primitive automedian triangle from a primitive Pythagorean triple using the Euclidean parameters m, n, then m>n and it follows that b \ge a \ge c. As non- primitive automedian triangles are multiples of their primitives the inequalities of the sides apply to all integer automedian triangles. Equality occurs only for trivial equilateral triangles. Furthermore, because m+n is always odd, all the sides a, b, c have to be odd.
The Miura fold is a form of rigid origami, meaning that the fold can be carried out by a continuous motion in which, at each step, each parallelogram is completely flat. This property allows it to be used to fold surfaces made of rigid materials. For instance, large solar panel arrays for space satellites in the Japanese space program have been Miura folded before launch and then spread out in space.. A folded Miura fold can be packed into a compact shape, its thickness reflecting only the thickness of the folded material. Folded material can be unpacked in one motion by pulling on its opposite ends, and likewise folded by pushing the two ends together.
On that date, the station also adopted the on-air imaging that Seattle sister station KSTW implemented when that station joined CBS four months earlier on March 13, which, in addition to the aforementioned parallelogram "11" logo design, was accompanied by that station's graphics package, set design and newscast theme music ("Millennium 3", a syndicated package composed by Shelly Palmer that was originally commissioned by Gaylord for KTVT and KSTW, which the former used until 1999). During the station's first decade with CBS, newscasts were added and dropped from KTVT's schedule. Channel 11 would first expand news programming with the debut of half-hour weekday newscasts at noon and 5:00 p.m.
If all five points are collinear, then the remaining line is free, which leaves 2 parameters free. Given four points in general linear position (no three collinear; in particular, no two coincident), there are exactly three pairs of lines (degenerate conics) passing through them, which will in general be intersecting, unless the points form a trapezoid (one pair is parallel) or a parallelogram (two pairs are parallel). Given three points, if they are non- collinear, there are three pairs of parallel lines passing through them – choose two to define one line, and the third for the parallel line to pass through, by the parallel postulate. Given two distinct points, there is a unique double line through them.
In the winter the doors of this place are thronged > with a crowd of sleighs and sleigh drivers, while inside, skaters and > spectators form a living, moving panorama, pleasant to look upon. The place > is lighted by gas, and men and women, old and young, with a plentiful > sprinkling of children, on skates, are practicing all sorts of gyrations. > The ladies are prettily and appropriately dressed in skating costumes, and > some of them are proficient in the art of skating. The spectators sit or > stand on a raised lege around the ice parallelogram, while the skaters dart > off, singly or in pairs, executing quadrilles, waltzes, curves, straight > lines, letters, labyrinths, and every conceivable figure.
However, an oval atop a shaded triangle, which sits next to another shaded triangle, which are both presented above a cylindrical glass stem, form a collection of shapes that are reminiscent of a martini glass in front of and to the left of the large bottle. The fork can be placed in the lower-right quadrant because of the short, curved black lines highlighted against a white parallelogram, indicating the prongs of the fork. Once the prongs are found, the viewer can make out the brown handle slightly below the prongs and separated from them by a small triangle. With the title objects placed within the painting, other objects also begin to emerge from the geometric contours.
The design suggested by the French maps is corroborated by the accounts of British and American visitors who travelled to Saigon seeking trade deals for their respective countries in the 1820s. British trade envoy John Crawfurd wrote that "the citadel of Saigon...is, in form, a parallelogram...I conjecture, from appearance, that the longest side of the square may be about three- quarters of a mile in length".Crawfurd, p. 223. George Finlayson, a naturalist and surgeon who travelled to southern Vietnam as a member of a trade delegation from the British East India Company, described the fortress as being "of square form, and each side is about half a mile in extent".
It would have been possible to connect F directly to the piston rod (the "Watt's linkage" design), but this would have made the machine an awkward shape, with G a long way from the end of the walking beam. To avoid this, Watt added the parallelogram linkage BCDE to form a pantograph. This guarantees that F always lies on a straight line between A and D, and therefore that the motion of D is a magnified version of the motion of F. D is therefore the point to which the piston rod DH is attached. The addition of the pantograph also made the mechanism shorter and so the building containing the engine could be smaller.
St Martin's Hall was built for John Hullah, in 1847, by William Cubitt, from a design by Richard Westmacott. The scheme was financed by subscription and it was built on a parallelogram of land, by wide, connected to a plot on Long Acre ( by ); and consisted of a main hall with connected anterooms, galleries and a 500-seat lecture hall.St. Martin's Music Hall 16 February 1850 The Builder, at Arthur Lloyd theatre history site, accessed 1 April 2008 It was built in the Elizabethan style, with a large domed iron roof. The music hall was capable of seating 3,000 persons and was opened in 1850 by Hullah, the founder of a new "school of choral harmony".
During the first interval of time, an object is in motion from point A to point B. Undisturbed, it would continue to point c during the second interval. When the object arrives at B, it receives an impulse directed toward point S. The impulse gives it a small added velocity toward S, such that if this were its only velocity, it would move from B to V during the second interval. By the rules of velocity composition, these two velocities add, and point C is found by construction of parallelogram BcCV. Thus the object's path is deflected by the impulse so that it arrives at point C at the end of the second interval.
Following the effects of the Great Depression, the project was shelved and adapted by Wright for the Price Company in 1952. Wright, therefore, plucked his "tree" out of the "crowded forest" of Manhattan skyscrapers and placed it on the Oklahoma prairie where it continues to stand uncrowded by neighboring tall buildings. The floorplan of the Price Tower centers upon an inlaid cast bronze plaque, bearing the logo of the Price Company and marking the origin of a parallelogram grid upon which all exterior walls, interior partitions and doors, and built-in furniture are placed. The resulting design is a quadrant plan—one quadrant dedicated for double-height apartments, and three for offices.
Constitutional provisions were also made for state-owned harbors with zones along the shore reserved for "landings, wharves and streets and other conveniences of navigation and commerce." All this was later modified to allow towns and municipalities to gain more control of their own shorelines, setting the stage for coherent plans for development and reclamation.. The arrangement of the "finger" piers on the Central Waterfront, each more or less a parallelogram, dates from an 1897 plan. Their uniform northeast-southwest direction was prescribed by city engineer Reginald H. Thomson and his assistant George F. Cotterill. Most earlier piers, none of which survive, formed a perfect right angle to the shore; the present piers do not.
Across the street, the federal government established its presence in the area with a Classical Revival post office built on part of the original Brisbane property. The unusual shape of the parcel required that the building be shaped like a parallelogram. In 1919, with the war over, the city and county built the Soldiers' Monument at the corner to the west of the courthouse, to memorialize not just its veterans from the recent war but those from the Civil War a half-century before as well. The statue of Emory Upton honors the memory of the most famous local soldier, whose innovative tactics led to a Union victory at the Battle of Spotsylvania Court House.
A kite is an orthodiagonal quadrilateral in which one diagonal is a line of symmetry. The kites are exactly the orthodiagonal quadrilaterals that contain a circle tangent to all four of their sides; that is, the kites are the tangential orthodiagonal quadrilaterals.. A rhombus is an orthodiagonal quadrilateral with two pairs of parallel sides (that is, an orthodiagonal quadrilateral that is also a parallelogram). A square is a limiting case of both a kite and a rhombus. Orthodiagonal equidiagonal quadrilaterals in which the diagonals are at least as long as all of the quadrilateral's sides have the maximum area for their diameter among all quadrilaterals, solving the n = 4 case of the biggest little polygon problem.
Both aircraft were single bay biplanes with wings of rectangular plan mounted with strong stagger. Both upper and lower wings were one-piece, two spar structures. Normally such wings were braced together on each side by a pair of interplane struts, one between each of the two corresponding upper and lower spars and stayed by incidence wires, but the de Marçays had instead rigid interplane braces of parallelogram form. The upper wing was supported over the fuselage with two pairs of N-form cabane struts and the lower one passed under the fuselage and was joined to it by three short struts, two to the forward spar linked to the engine mounting and the other, centrally, to the rear.
"Squat" occurs because the top of the final drive chain run pulls the swingarm upwards; "Shaft-jacking" occurs because the shaft drive bevel gear tries to "climb up" the large bevel gear in the wheel hub, thereby pushing the swingarm downwards and away from the frame."Motorcycle Handling and Chassis Design: The Art and Science" -Tony Foal Shaft-jacking can be minimised by devices such as parallelogram swingarms. A practical way to minimise squat on a chain-drive bike is to locate the final drive sprocket as close as possible to the axis of the swingarm pivot; the ideal solution is to make the final drive sprocket and the swingarm pivot concentric, as was done on the Hesketh V1000.
Beginning October 1, 2001, in direct response to the September 11 attacks, the first hour was referred to as Raw instead of Raw Is War and the second hour changed from the War Zone to the Raw Zone by the show's on-screen graphics; however, announcers would generally refer to the entire two-hour block as Raw on-air. Raw updated to a new, industrial-inspired, parallelogram-shaped TitanTron in 2002. When the War ended, they began advertising their website on the ring aprons instead. They occasionally used black ropes. Like the previous set, the TNN logo was relocated to the bottom side of the TitanTron which was then replaced by the Spike TV logo on August 11, 2003 upon network relaunch.
Other interesting facets of the house include a long screened in patio (the roof of the patio is a screen as well, not a roof), a swimming pool only a few feet from the master bedroom door, an unusually shaped built-in bed in the master bedroom and triangle-shaped recessed lighting bays. As he often did, Wright designed all the furniture himself, with most of it anchored to the walls, so the homeowners couldn't even rearrange it. He drew parallelogram bunk beds and a bed for the tiny, prow-shaped master bedroom, and a fabulous, funny little mini-bar. He drew a half-octagon dining room table that attached to a wall, with rolling stools so low to the ground that they seem built for children.
Let A, B, C be the vertices of a right triangle, with a right angle at A. Drop a perpendicular from A to the side opposite the hypotenuse in the square on the hypotenuse. That line divides the square on the hypotenuse into two rectangles, each having the same area as one of the two squares on the legs. For the formal proof, we require four elementary lemmata: # If two triangles have two sides of the one equal to two sides of the other, each to each, and the angles included by those sides equal, then the triangles are congruent (side-angle-side). # The area of a triangle is half the area of any parallelogram on the same base and having the same altitude.
The length of the typical motorcycle fork means that they act as large levers about the headstock requiring the forks, the headstock, and the frame to be very robust adding to the bike's weight. Hub-center steering systems use an arm, or arms, on bearings to allow upward wheel deflection, meaning that there is no stiction, even under braking. Braking forces can be redirected horizontally along these arms, or tie rods, away from the vertical suspension forces, and can even be put to good use to counteract weight shift. Finally, the arms typically form some form of parallelogram which maintains steering geometry over the full range of wheel travel, allowing agility and consistency of steering that forks currently cannot get close to attaining.
Engraving of the palace published in the volume X of Diccionario geográfico-estadístico-histórico de España y sus posesiones de ultramar by Pascual Madoz, in 1850. Its plant formed a rectangle parallelogram, consisting each of its four facades of three floors that were in all them in the same horizontal plan, serving as entrance to the building a spacious garden, which occupied the site of the old Convento de la Natividad y San José A portal with three entries, ornate with pillars, separated this garden from the Calle de Alcalá. The building dates from early 19th century. It was built as a dowry for the Duchess of Abrantes, for which circumstance was designated with the name of "la casa de los alfileres" (the house of the pins).
Somewhat unusual for a market this size was that two AM stations dominated the radio landscape, both with programming that included highly competitive news departments. Its advantage over longtime crosstown rival WHLS (a single tower 1000 watt "Local" station) was its powerful "Regional" signal of 5,000 watts, boasting seven towers (six-tower parallelogram daytime, 4 towers inline at night), able to reach listeners north of Port Huron, known as the Thumb area. For this reason, the station was billed for years as "The Big Station in Michigan's Thumb". WPHM had maintained a longtime agreement with the ABC radio network and the Associated Press, which gave the station the tools it needed to be a strong local news competitor against WHLS and sister station WSAQ.
Schnabel returned to Houston in 1975 and rented a studio in the Heights neighborhood. After reported, repeated badgering by the artist, Jim Harithas, director of the Contemporary Arts Museum Houston, agreed to give him a show. The eponymously titled exhibit ran from February 20 to March 7, 1976 in the parallelogram building's lower gallery. On seeing the show, ARTnews critic Charlotte Moser wrote, “Though still formative, Schnabel’s paintings possess a palpable presence,” but found the work “clearly influenced by post-minimalist artists whose intellectual ideas he might share but whose technical expertise and clarity of vision he has yet to acquire.” It was with his first solo show, at the Mary Boone Gallery in 1979 that Schnabel had his breakthrough; all his works were sold in advance.
A seat that is not held in place properly can be dangerous if not at least uncomfortable and annoying. Newer and better designs of the piston style seat post have minimized all forms of wiggle and seatposts with actual adjustable pistons built into the post are even available. Parallelogram suspension seat posts use dual linked bars that connect the saddle clamp to the post, and all operate in an arcing motion although some arc backwards and others arc forwards. Differences between the arc directions create posts that are designed for different things, a rear arc would be better for small wheels, moving fast or going uphill while a forward direction would be best with larger wheels on a downhill or at slower speeds.
Many metals have several different crystal structures at the same composition, but most metals do not show this shape-memory effect. The special property that allows shape-memory alloys to revert to their original shape after heating is that their crystal transformation is fully reversible. In most crystal transformations, the atoms in the structure will travel through the metal by diffusion, changing the composition locally, even though the metal as a whole is made of the same atoms. A reversible transformation does not involve this diffusion of atoms, instead all the atoms shift at the same time to form a new structure, much in the way a parallelogram can be made out of a square by pushing on two opposing sides.
During the reign of Emperor Ashoka in the 3rd century BCE, it was one of the world's largest cities, with a population of about 150,000–400,000. The city is estimated to have had a surface of 25.5 square kilometers, and a circumference of 33.8 kilometers, and was in the shape of a parallelogram and had 64 gates (that is, approximately one gate every 500 meters). Pataliputra reached the pinnacle of prosperity when it was the capital of the great Mauryan Emperors, Chandragupta Maurya and Ashoka. The city prospered under the Mauryas and a Greek ambassador, Megasthenes, resided there and left a detailed account of its splendour, referring to it as "Palibothra": Mauryan remains of a wooden palisade discovered at the Bulandi Bagh site of Pataliputra.
The Ambrose–Singer theorem (due to ) relates the holonomy of a connection in a principal bundle with the curvature form of the connection. To make this theorem plausible, consider the familiar case of an affine connection (or a connection in the tangent bundle -- the Levi-Civita connection, for example). The curvature arises when one travels around an infinitesimal parallelogram. In detail, if σ: [0, 1] × [0, 1] → M is a surface in M parametrized by a pair of variables x and y, then a vector V may be transported around the boundary of σ: first along (x, 0), then along (1, y), followed by (x, 1) going in the negative direction, and then (0, y) back to the point of origin.
In New York City, as Broadway crisscrosses major avenues, the resulting blocks are cut like triangles, and buildings have been built on these shapes; one such building is the triangularly shaped Flatiron Building which real estate people admit has a "warren of awkward spaces that do not easily accommodate modern office furniture" but that has not prevented the structure from becoming a landmark icon. Designers have made houses in Norway using triangular themes. Triangle shapes have appeared in churches as well as public buildings including colleges as well as supports for innovative home designs. Triangles are sturdy; while a rectangle can collapse into a parallelogram from pressure to one of its points, triangles have a natural strength which supports structures against lateral pressures.
In any convex quadrilateral ABCD, the sum of the squares of the four sides is equal to the sum of the squares of the two diagonals plus four times the square of the line segment connecting the midpoints of the diagonals. Thus : a^2 + b^2 + c^2 + d^2 = p^2 + q^2 + 4x^2 where x is the distance between the midpoints of the diagonals. This is sometimes known as Euler's quadrilateral theorem and is a generalization of the parallelogram law. The German mathematician Carl Anton Bretschneider derived in 1842 the following generalization of Ptolemy's theorem, regarding the product of the diagonals in a convex quadrilateralAndreescu, Titu & Andrica, Dorian, Complex Numbers from A to...Z, Birkhäuser, 2006, pp. 207–209.
Two isometry groups are said to be equal up to conjugacy with respect to affine transformations if there is an affine transformation such that all elements of one group are obtained by taking the conjugates by that affine transformation of all elements of the other group. This applies for example for the symmetry groups of two patterns which are both of a particular wallpaper group type. If we would just consider conjugacy with respect to isometries, we would not allow for scaling, and in the case of a parallelogrammetic lattice, change of shape of the parallelogram. Note however that the conjugate with respect to an affine transformation of an isometry is in general not an isometry, although volume (in 2D: area) and orientation are preserved.
The tracks "It's All True," "If I Could Talk I'd Tell You" (cowritten by Eugene Kelly of the Vaselines), and "The Outdoor Type" were released as singles in the UK. "Purple Parallelogram," a song written by Dando and Oasis's Noel Gallagher, was originally included on promotional copies of Car Button Cloth between "Something's Missing" and "Knoxville Girl," but was reportedly removed at Gallagher's request. The album would be the last studio release from The Lemonheads for a decade, when they released a long-awaited self- titled follow-up, while in the meantime the group's frontman and sole remaining original member, Evan Dando, issued his first official solo album, 2003's Baby I'm Bored (a live album and EP were released in Australia two years earlier).
Addition and multiplication of real numbers are defined in such a way that expressions of this type satisfy all field axioms and thus hold for . For example, the distributive law enforces : It is immediate that this is again an expression of the above type, and so the complex numbers form a field. Complex numbers can be geometrically represented as points in the plane, with Cartesian coordinates given by the real numbers of their describing expression, or as the arrows from the origin to these points, specified by their length and an angle enclosed with some distinct direction. Addition then corresponds to combining the arrows to the intuitive parallelogram (adding the Cartesian coordinates), and the multiplication is -less intuitively- combining rotating and scaling of the arrows (adding the angles and multiplying the lengths).
Rather than the preceding "turntable" steering, where both front wheels turned around a common pivot, each wheel gained its own pivot, close to its own hub. While more complex, this arrangement enhances controllability by avoiding large inputs from road surface variations being applied to the end of a long lever arm, as well as greatly reducing the fore- and-aft travel of the steered wheels. A linkage between these hubs pivots the two wheels together, and by careful arrangement of the linkage dimensions the Ackermann geometry could be approximated. This was achieved by making the linkage not a simple parallelogram, but by making the length of the track rod (the moving link between the hubs) shorter than that of the axle, so that the steering arms of the hubs appeared to "toe out".
Just as Plus adds Diamonds and Advanced adds Hourglasses, Challenge dancing adds new formations which have their own rules for circulation as well as calls that apply specifically to them. Additional formations include Butterflies, Galaxies, Triangles, Xs, and Zs. Also, many formations used at lower levels are extended to include cases where they are "distorted" – while they have the same number of dancers and the dancers follow the same rules of interaction, they are not spaced the same way. For example, a wave may be "offset" so that the two halves are not lined up with each other, or a "parallelogram" consisting of two lines offset from each other can be considered to be two "boxes" even though the dancers in each box are not adjacent to each other. Irregular distortions, e.g.
An employee of the HBC, wrote a general description of Fort Vancouver and its structural composition as it was in 1843: > The fort is in the shape of a parallelogram, about 250 yards long, by 150 > broad; enclose by a sort of wooden wall, made of pickets, or large beams > firmly fixed in the ground, and closely fitted together, twenty feet high, > and strong secured on the inside by buttressess. At each angle there is a > bastion, mounting two twelve pounders, and in the centre there some eighteen > pounders; ... these cannon have become useless. The area within is divided > into two courts, around which are arranged about forty neat, strong wooden > buildings, one story high, designed for various purposes... The fort was substantial. The palisades that protected it were long, wide and about high.
The Dominant II (introduced in 1976) had a deeper windscreen, rectangular headlights, a different grille and a smaller, flat rear window. The Dominant III was designed to satisfy a Scottish Bus Group requirement for express coaches, and featured shallow, parallelogram-shaped flat double-glazed side windows similar to those on SBG's previous Alexander M-type coaches. Most Dominant IIIs featured a small Dominant I style windscreen mounted in the lower Dominant II position so as to allow a destination display to be included without breaking the roof line, but others had full-height Dominant II type windscreens. The small high-level windows were designed for SBG's overnight Scotland to London services where quietness was more important than passenger views, but nevertheless some other operators did buy the Dominant III as a touring coach.
The text reading "Basic Pokémon" is now directly under the HP (Hit Points) instead of the upper-left corner. The information about the Pokémon directly below the illustration is now in a parallelogram instead of a rectangle. Two cards from this set were banned from tournament play: Sneasel and Slowking. It was at this point the 2 different play formats were realized: Unlimited (allowing all cards to be played), and Limited where only the Neo Genesis cards could be played (this limited format would go through a few changes where as more sets were released where the rules were changed to "Neo Genesis and newer cards are allowed to be played in official tournaments" this would later be changed to be "only the 8 most recent sets are legal for tournament play").
United States Parcel Post Station, also known as the Railway Express Building, is a historic post office structure located at Baltimore, Maryland, United States. It is two stories high with the first floor at the St. Paul Street level and is supported by concrete piers that extend 35 feet down to the level of the Jones Falls Expressway (I-83). It was constructed in 1929 in a Classical Revival style and built of reinforced concrete with brick walls and limestone and terra cotta trim, the building is a parallelogram in plan, measuring 142 feet on the east and west and 269 feet deep. The principal facade features a 4 foot high limestone base and terra cotta capitals molded in the form of an American bald eagle within a wreath.
The city could be split into two different sections: an upper "acropolis" and a "lower town". The lower town consisted of lower valued residential building located on the eastern side of the city, while the upper acropolis would be on the western side of the city which contained of the higher value buildings and public buildings. The acropolis was a “parallelogram that was 400–500 yards north-south and 200–300 yards east-west” It was also thought that the acropolis area would be built on the highest part of the mound in the city showing the importance and status of the area was much higher than the rest of the area. Another feature which suggests the acropolis is of higher importance is that the fortifications around the area where bigger and stronger than those around the rest of the city.
The original 1380 building was a simple parallelogram measuring externally 36 feet by 46 feet, containing a single large room, a great hall, extending up to the roof, lit by four 12 foot pointed-arched gothic windows, two on each of the long sides. The original entry door survives in the middle of the northern façade, but the two 12 foot flanking windows were later filled in, although their outlines are still visible in the stonework. The fireplace was at the western end and the dais on which was situated the lord's table was at the opposite eastern end, beyond which was the screens-passage leading to the domestic outbuildings. A private chamber for the lord's private occupation was built over the screens-passage, but extended partially into the great hall as a gallery, leaving most of it still open to the roof.
The occurrence of a prominent mastoid process tends to push the concha forward, which extends the pinna (external ear) away from the side of the head. The external ear is mounted upon the bony base of the underlying temporal bone, therefore, anomalies and asymmetries of the skeletal shape can cause either pinna, or both pinnae, to become prominent. In relation to the protruding mastoid process, the most recognizable skeletal anomaly is the change in the position and in the projection of the pinna, as associated with non-synostotic plagiocephaly (the positional flattening of the side of the head, not caused by the inappropriate union of two bones). Hence, in the occurrence of a flattening of the skull (parallelogram deformation of the cranial vault), the side of the head afflicted with occipital plagiocephaly presents a prominent ear.
The fundamental rectangle in the complex plane of u There are twelve Jacobi elliptic functions denoted by pq(u,m), where p and q are any of the letters c, s, n, and d. (Functions of the form pp(u,m) are trivially set to unity for notational completeness.) u is the argument, and m is the parameter, both of which may be complex. In the complex plane of the argument u, the twelve functions form a repeating lattice of simple poles and zeroes. Depending on the function, one repeating parallelogram, or unit cell, will have sides of length 2K or 4K on the real axis, and 2K' or 4K' on the imaginary axis, where K=K(m) and K'=K(1-m) are known as the quarter periods with K(.) being the elliptic integral of the first kind.
It follows that the intersections of al such segments occur at the same point. Translating that point to the origin, it follows that the polygon is centrally symmetric; that is, if a point z is in the polygon, so too is −z. It is easy to see translates of a centrally symmetric convex hexagon tessellate the plane. If A is a point of the hexagon, then the lattice is generated by the displacement vectors AB and AC where B and C are the two vertices which are not neighbours of A and not opposite A. Indeed, the second picture shows how the hexagon is equivalent to the parallelogram obtained by displacing the two triangles chopped off by the segments AB and AC. Equally well the first picture shows another way of matching a tiling by parallelograms with the hexagonal tiling.
Faulting in either setting is reliant on the lock-up and strain accumulation of a fold typically at its critical angle. Asymmetric folding develops in the forelimb (the limb furthest from the source of thrust) of the fold and may either absorb strain into or transmit strain through the stratigraphic units composing the fold. A system that absorbs strain is recognized as a trishear zoneZehnder, A. T. and Allmendinger, R. W. (2000) Velocity field for the trishear model, Journal of structural Geology, 22, 1009-1014 being triangular in shape; while a parallel deformation zone transmits shear across the units of the fold and typically takes on the form of a parallelogram or is rectangular in geometry. These two deformation patterns may exist in a single fold and at some time during continued deformation may reconnect with the detachment.
The ES-175 is a single- or dual-pickup archtop electric guitar made by Gibson. Unlike Gibson's L5 and Super 400 guitars, the ES-175 typically has an all-laminate construction, which allows the cost of materials and construction to be kept down, as well as assisting in keeping feedback at higher volumes manageable. The ES-175 has a rosewood fingerboard with parallelogram inlays, a 3" deep body, a floating bridge, one or two humbuckers (current models are equipped with Gibson's 57 Classic pickups, replicas of the PAF pickups from the late 1950s), 20 frets (earlier models had 19 frets) and independent volume and tone controls for each pickup. The guitar has the standard Gibson scale length of 24.75" and normally has a sunburst and natural finish, though Gibson has produced limited runs in black, white, and wine red.
In engineering, iso-elastic refers to a system of elastic and tensile parts (springs and pulleys) which are arranged in a configuration which isolates physical motion at one end in order to minimize or prevent similar motion from occurring at the other end. This type of device must be able to maintain angular direction and load-bearing over a large range of motion. The most prominent use of an iso-elastic system is in the supporting armature of a Steadicam, used to isolate a film or video camera from the operator's movements. Steadicam arms all work in a fashion similar to a spring lamp since each arm has two sections (similar to and labelled like a human arm); both the upper and fore-arm sections consist of a parallelogram with a diagonal iso- elastic cable-pulley-spring system.
The best kind of city is one which is about a mile long by half a mile broad, built in the form of a parallelogram, facing the northeast, and surrounded by a high wall and ditch. A hamlet should be a Yojana distant from a city: a village half a Yojana from a hamlet. The roads leading to the cardinal points from a city should be twenty Dhanus (above 100 feet) broad: a village road should be the same: a boundary road ten Dhanus: a royal or principal road or street should be ten Dhanus (above fifty feet) broad: a cross or branch road should be four Dhanus. Lanes and paths amongst the houses are two Dhanus in breadth: footpaths four cubits: the entrance of a house three cubits: the private entrances and paths about the mansion of still narrower dimensions.
The town was originally shaped as a parallelogram covering twenty-six blocks for a total of 304 housing lots. During the summer of 1853, lots sold rapidly, commanding prices varying from $50 to $150 each. On New Year's Day 1854, track was laid, and railway cars began running between Freeport and Warren. The population began to grow, mostly with English and Irish residents. In 1854, there were about a dozen families in Lena. During the summer of 1855, Reber & Cheney and Dodds erected a three-story brick building at the corner of Railroad and Schuyler streets. It was completed in the fall of 1856 at a cost of about $4,000. The building is still used by local businesses. The Panic of 1857 had little effect on the growth of the town, and rapid expansion continued through 1860.
Starting with the 2004 postseason, Fox's baseball broadcasts began using the same graphics package that debuted with NFL telecasts in 2003. The score banner was changed to match the layout adopted by the network's football coverage at the start of the 2004 season, but using the abbreviations of the teams playing instead of their logos. Team abbreviations were shown this time in electronic eggcrate lettering in the team's main color, the shaded area above the score banner was removed, and the scores were shown in white text in black parallelograms. Whenever team- specific information was displayed in the banner such as a scored run or an out, the abbreviation would morph into the team logo with the scored run being displayed; the team who would score a run would have its abbreviation morph into its logo and a "strobe light" would flash over the black parallelogram as the score changes.
It can be verified by dividing the polygon into triangles, and can be considered to be a special case of Green's theorem. The area formula is derived by taking each edge AB, and calculating the area of triangle ABO with a vertex at the origin O, by taking the cross-product (which gives the area of a parallelogram) and dividing by 2. As one wraps around the polygon, these triangles with positive and negative area will overlap, and the areas between the origin and the polygon will be cancelled out and sum to 0, while only the area inside the reference triangle remains. This is why the formula is called the surveyor's formula, since the "surveyor" is at the origin; if going counterclockwise, positive area is added when going from left to right and negative area is added when going from right to left, from the perspective of the origin.
The top retracts in three stages: over the two front passengers, overall four passengers (to the rear spoiler), and fully retracted with its stack folded behind the rear head restraints just above the rear cargo opening. The top is controlled either via the key remote or by open/close buttons at the windshield header adjacent to the interior ceiling light and retracts to the first two stages at speeds up to 60 km/h (37 mph), to its third stage at up to 50 mph -- and is available in black, tan or red. With its 50/50 split-fold rear seats in their upright position, the 500C rear cargo capacity is reduced from 9 cubic feet to 5.4 feet compared to the hatchback -- offering 23.4 cubic feet cargo volume with the 50/50 split-fold rear seats folded. At its rear trunk lid, the 500C features "parallelogram" liftgate hinges.
The antiparallelogram is an important feature in the design of Hart's inversor, a linkage that (like the Peaucellier–Lipkin linkage) can convert rotary motion to straight-line motion.. An antiparallelogram-shaped linkage can also be used to connect the two axles of a four-wheeled vehicle, decreasing the turning radius of the vehicle relative to a suspension that only allows one axle to turn.. A pair of nested antiparallelograms was used in a linkage defined by Alfred Kempe as part of his universality theorem stating that any algebraic curve may be traced out by the joints of a suitably defined linkage. Kempe called the nested-antiparallelogram linkage a "multiplicator", as it could be used to multiply an angle by an integer. Antiparallelogram braced to stop it turning into a normal parallelogram. The points PQRS are the midpoints of the sides and are collinear, and X can be any distance away on the perpendicular bisector of SQ. With this linkage .
Team abbreviations were shown this time in electronic eggcrate lettering in the team's main color, the shaded area above the score banner was removed, and the scores were shown in white text in black parallelograms. Whenever team-specific information was displayed in the banner such as a scored run or an out, the abbreviation would morph into the team logo with the scored run being displayed; the team who would score a run would have its abbreviation morph into its logo and a "strobe light" would flash over the black parallelogram as the score changes. When a home run was displayed in the banner, a split "strobe light" would flash a few times across the banner with the words "HOME RUN (team)" in the team's color then zooming in to the center from both left and right angles, accompanied by two distorted electric buzzes followed by a futuristic computer sounder. This marked the first time that a home run was displayed in the banner.
4 World Trade Center reflecting water of the Hudson River, viewed from One World Observatory in 2017 The above-ground portion of the building dedicated for retail use (which consists of the ground floor, the three floors immediately above the ground floor as well as the two floors below ground), accommodates offices using two distinct floor shapes. From floors 7 through 46, the typical floor space is 36,350 square feet (3,376 square meters) in the shape of a parallelogram (which is designed to echo the configuration of the site). From floors 48 through 63 the floor space is 28,000 sq ft (2,600 square meters) in the shape of a trapezoid, shaped so that it opens toward the tip of Manhattan Island and also triangulated to face One World Trade Center. The tower includes five levels of mechanical floors. The New York Power Authority selected UTC Power to provide 12 PureCell Model 400 fuel cells that will be used to provide electricity, water and heat.
The parabola is bounded by two pink brick walls which slope backwards from the two corners of the overall façade, creating voids either side of the parabola, and it also has a floating canopy either side of its apex covering these voids. The side walls of the church are strongly zig-zag, with six triangular projections running from ground to roof on each side in the same pink brick, with small square windows inserted into the otherwise blank wall in an array shaped like a parallelogram on each of the overall twenty-four faces of this arrangement. The roof has a shallow downward curve on either side of the major axis, over these projections, and over the nave is shaped as a result like a row of six and a half lozenges (the half is the canopy over the entrance parabola). At the altar end, the roof forms an irregular hexagon stretched transversely and with the angle behind the altar smoothed away by the apse curve.
In 1697, King William III granted by Royal Charter, Van Cortlandt Manor to his grandfather, Stephanus Van Cortlandt. Originally, it was a tract stretching from the Hudson River on the west to the first boundary line between the Province of New York and the Colony of Connecticut, on the east, twenty English miles in length by ten in width, in shape nearly a rectangular parallelogram, forming, "The Manor of Cortlandt." The massive holding was acquired by direct purchase from the Indians, in part, by Stephanus van Cortlandt, a native born Dutch gentleman of New York, and in part by others whose titles he subsequently bought, this tract, together with a small tract on the west side of the Hudson River opposite the promontory of Anthony's Nose, which he also purchased from the Indians. The Van Cortlandt Manor House was built sometime before 1732 but was not any owner's principal residence until Pierre moved there in 1749.
The western Alborz itself, to the east of the Safid-rud valley, is wider and more intricate, with three parallel (WNW-ESE) ranges; the southernmost and lowest one is represented in Gilan by the Asman-sara Kuh in the Ammarlu district; the medium one is the most continuous, from the Kuh-e- Dalfak to the Keram Kuh, whereas the transverse valley of Polrud clearly divides the northern range into Kuh-e-Natesh and Kuh-e-Somam or Somamus, the highest spot of Gilan. All these mountains have a very complicated geological structure and tectonic history which connects them to the structural complex of central Persia. Though all those mountains cover a greater area than the plains, these are the most specific feature of the province, and locally, the word Gilan often refers to the plain areas or particularly to the central plain. This large parallelogram of lowlands is heterogeneous and can be divided into two main parts: the delta of the Safid-rud in the east and the Fumanat plain in the west.
The first site is known as Romancamp Gate, and lies 100 metres to the north east of the old church of Bellie, with a cliff to the north west that lies on the east bank of the River Spey. The site was recorded by the antiquarian George Chalmers in 1799 as "the remains of the Roman encampment overlooking the low ground by the river ... on plan nearly a rectangular parallelogram of 888' by 333', but the W and most of the N sides have been destroyed." In the mid 20th century O. G. S. Crawford noted that the enclosure's size would make it considerably smaller than any other known Roman camp in Scotland and felt that the lack of identified gates counted against it being Roman, but also acknowledged that it was difficult to assign it to any other period. Air investigation in 1943 revealed cropmarks of ditches, including a rounded corner at the south west, but the site was extensively damaged during World War II by the construction of a military camp including emergency stone shelters.
A masonry skew arch bridge photographed shortly after its completion in 1898, showing the helicoidal nature of its stonework A skew arch (also known as an oblique arch) is a method of construction that enables an arch bridge to span an obstacle at some angle other than a right angle. This results in the faces of the arch not being perpendicular to its abutments and its plan view being a parallelogram, rather than the rectangle that is the plan view of a regular, or "square" arch. In the case of a masonry skew arch, the construction requires precise stonecutting, as the cuts do not form right angles, but once the principles were fully understood in the early 19th century, it became considerably easier and cheaper to build a skew arch of brick. The problem of building skew arch masonry bridges was addressed by a number of early civil engineers and mathematicians, including Giovanni Barbara (1726), William Chapman (1787), Benjamin Outram (1798), Peter Nicholson (1828), George Stephenson (1830), Edward Sang (1835), Charles Fox (1836), George W. Buck (1839) and William Froude (c. 1844).
He also planned to build nine symmetrical public squares, quays, vast and long boulevards or avenues bordered by trees and perfectly ventilated, fountains, arcades, green areas round the Patras Castle and three main doors which would open on the roads to Gastouni, Kalavryta and Corinth. Voulgaris also wanted to cover out of his own poecket the financial costs for tree planting in Patras. However, the original plan was not fully implemented, because on the one hand the kodjabashis (notables and primates) and the local property owners put Governor Kapodistrias under pressure to prevent any change, and on the other hand state finances were not sufficient to achieve Voulgaris' visionary plan: in 1830, the 5 symmetrical squares he had designed in the parallelogram bordering the coastal area were reduced to 2 only, including the central square dedicated to democracy (currently Vasileos Georgiou I Square) and concord (currently Vasilissis Olgas Square). alt= After handing over the city's plans to Governor Kapodistrias, Voulgaris joined the troops of the regular Greek army, then commanded by the governor's brother, Augustinos Kapodistrias, commander-in-chief for Continental Greece.

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