104 Sentences With "traced out" | Random Sentence Generator

The same image as above, with the filaments traced out.

The Fed's decision traced out a long-term vision for meager growth.

These larger hexagons become the individual units, rather than the small hexagons traced out by the carbon atoms.

"On top of that, what we'll see is Nvidia has traced out the classic three wave corrective pattern," he said.

When the motions of thousands of bacteria were averaged, they traced out regular ellipses that were many times larger than the individual bacteria.

Additionally, if you pretended that the Dragon were an arc and traced out the full circle, you could determine how much mass caused the warp.

The latest data (February 2016) show that the ECB's broad monetary aggregate, M3, remains on a stable 5 percent growth path traced out since last summer.

In this user's edits, they traced out the inability of the developers to answer this question as a sign that they didn't have a good one.

If you zoomed in, you'd see that each of those coiling lines is traced out by the smallest binary systems, with the individual stars spinning around each other.

Do you need any further convincing that the Fed is hopelessly behind the curve traced out by an accelerating economy about to be turbo-charged by Trump's tax cuts?

With a bright green digital marker, the friend traced out a route that, if all went to plan, would allow Nick and his friends to pull off an improbable rescue.

"For the most part, the scenario I just traced out is one that does not make the oil companies investible, but it does make everyone else a little better off," Cramer said.

With all those parallels to the late-'90s traced out, it's important to point out several crucial differences, which together make the current market seem less overheated and hazardous than, say, 1999.

Each corner on the route traced out for this sojourn in the midst of the mountain range that separates the Indian subcontinent from the Tibetan Plateau harbours the promise of an incredible panorama.

"Christmas in Oakland," from Advance Base's 2012 LP A Shut-In's Prayer, has been on my list for the last two-and-a-half weeks, and I'd roughly traced out its contours already.

Downturns and subsequent recoveries associated with the East Asian financial crisis of 22018/219, the global financial crisis of 21999/22000 and the shale bust of 22007/208 can all be traced out clearly in the spreads.

For more than three centuries, stock markets have traced out booms and busts regardless of any actions or non-actions by presidents, prime ministers, kings, Fed chairmen, Plunge Protection Teams, Congress, NEC directors or White House economic advisors.

Read MoreGood day in retail, but it's still eyeing longest weekly losing streak since '08 "Over the last 2½ years, it's traced out this pretty big and pretty bearish ominous pattern," he said Thursday on CNBC's "Trading Nation, " referring to the XRT.

Sitting inside the Dairy Godmother, the renowned frozen custard shop she opened 16 years ago on Mount Vernon Avenue, she traced out what was: the boarded-up bank now open for business, a biker bar down the street and the drug deals that would happen behind a nearby rent-a-room place.

So on July 22, when Sagittarius A* flared, the light collected by each scope traveled through a Rube Goldberg–like setup of mirrors and fiber-optic cables that traced out a path with a total length that varies no more than 1/1,000th the width of a hair, said Frank Eisenhauer, a physicist at Max Planck in Garching and the leader of GRAVITY.

That first morning I went to the beach my friends had said they always went to, Platis Gialos, where, after I noticed the pictures I tried to take of the landscapes all seemed to make everything small and dull, I finally took the notebook out, and a pen, and traced out the horizon in front of me without looking at the page, an old drawing class exercise.

The shape traced out by the rotating Reuleaux triangle covers approximately 98.77% of the area of the square..

The idea is based on the world lines traced out across spacetime by every electron. Rather than have myriad such lines, Wheeler suggested that they could all be parts of one single line like a huge tangled knot, traced out by the one electron. Any given moment in time is represented by a slice across spacetime, and would meet the knotted line a great many times. Each such meeting point represents a real electron at that moment.

Something has stimulated [感] them. When a picture is > traced out with the ashes of reeds, the moon's halo has a [corresponding] > gap. When the leviathan dies, comets appear. Something has moved them.

Note: Newton simply describes the arcs IH and KL as 'minimally small' and the areas traced out by the lines IL and HK can be any shape, not necessarily elliptic, but they will always be similar.

Yet, from an aerial map, the former route can be vaguely traced out; from the ground, very little can be seen of the second steam railroad to service Richmond as it has been overgrown by shrubs, trees, and other plant life.

Concurrently, the typhoon stalled and traced out a clockwise loop for roughly a day before resuming a course towards the northwest. Gradual weakening ensued, and the system transitioned into an extratropical cyclone after May 12; the system would dissipate three days later.

14, 1946), pp.85-95. Morris's system of signs emphasizes the role of stimulus and response in the orientation, manipulation, and consummation phases of action. His mature semiotic theory is traced out in Signs, Language, and Behavior (1946).Morris, Charles W.: Signs, Language and Behavior.

In July 2009, more than 40 people were killed in a fire accident in a firecracker unit. The police traced out unregistered units and irregularities that led to the accident. In a fire accident in August 2011, seven people were killed and five were seriously injured.

Butterfly joints are often made using a bandsaw. The piece of wood must be cut out, then sanded down to the proper size. The joint is then traced out onto another piece of wood. This piece of wood is what the end project will be made out of.

Board size varies from region to region. In Ningxia, the game is played on a 7×8 gridded board using black and white Go stones, 28 stones per player. The game is popular in agricultural communities in Northwestern China, and often played on a board traced out on the ground.

Bowen was the eldest son of James Bowen, painter and topographer, of Shrewsbury, where the younger Bowen was born. Bowen studied local antiquities under his father; traced out the pedigrees of Shropshire families, and became skilful in deciphering and copying ancient manuscripts. He died on 19 June 1832, aged 76.

As b varies smoothly between these two extremes, all the in-between points on the contract curve are traced out. Note that the above optimizations are not ones that the two people would actually engage in, either explicitly or implicitly. Instead, these optimizations are simply a way for the economist to identify points on the contract curve.

Marx, Capital, Volume I, Penguin ed. 1976, p. 273. Marx claimed that the origin of the money-form of value had never before been explained by bourgeois economics, and that "the mystery of money will immediately disappear" once the evolution of value-relations has been traced out from its simplest beginnings.Karl Marx, Capital, Volume I, Penguin 1976, p. 139.

Early on in his research (circa 1831), Faraday calls the patterns of apparently continuous curves traced out in metallic filings near a magnet magnetic curves. Later on he refers to them as just an instance of magnetic lines of force or simply lines of force.Faraday's Experimental Researches in Electricity: The First Series, Howard J. Fisher, 2004, Green Lion Press, p. 22 et al.

His frequent use of geometrical illustrations affords no evidence at all in support of a purely logico- mathematical interpretation of his philosophy; for Spinoza regarded geometrical figures, not in a Platonic or static manner, but as things traced out by moving particles or lines, etc., that is, dynamically.Cf. Marcello Colitti, Etica e politica di Baruch Spinoza, Aliberti, 2010, esp. s.v. "Etica".

In a blast in 1991 in a factory, 39 people were killed and 65 others were injured. In July 2009, more than 40 people were killed in a fire accident in a firecracker unit. The police traced out unregistered units and irregularities that led to the accident. In a fire accident in August 2011, seven people were killed and five were seriously injured.

Analogously, the world lines of test particles in free fall are spacetime geodesics, the straightest possible lines in spacetime. But still there are crucial differences between them and the truly straight lines that can be traced out in the gravity-free spacetime of special relativity. In special relativity, parallel geodesics remain parallel. In a gravitational field with tidal effects, this will not, in general, be the case.

Strings are also sometimes studied in nuclear physics where they are used to model flux tubes. As it propagates through spacetime, a string sweeps out a two-dimensional surface called its worldsheet. This is analogous to the one- dimensional worldline traced out by a point particle. The physics of a string is described by means of a two-dimensional conformal field theory associated with the worldsheet.

The length of M is called the proper time of the worldline or particle. If the worldline M is a line segment, then the particle is said to be in free fall. A world line traces out the path of a single point in spacetime. A world sheet is the analogous two-dimensional surface traced out by a one-dimensional line (like a string) traveling through spacetime.

In 1593, the leader of the mining community, Gaspar de Solís, under orders from the viceroy, created the first parish for the indigenous, and traced out the first blocks of a formal Spanish town. In 1603, it was formally established. Around this time, chapels such as the Nuestra Señora del Carmen and San Lorenzo were constructed. The monastery and church of San Francisco was also established.

Their method consisted of a rapidly rotating glass cylinder which, after being coated with lamp black, was placed next to the stretched rubber sample. Styli, attached to the mid-point and free end of the rubber sample, were held in contact with the glass cylinder. Then, as the free end of the rubber snapped back, the styli traced out helical paths in the lamp black coating of the rotating cylinder.

The proportionality is seen by the fact that the ratio for Jupiter, 5.23/11.862, is practically equal to that for Venus, 0.7233/0.6152, in accord with the relationship. Idealised orbits meeting these rules are known as Kepler orbits. The lines traced out by orbits dominated by the gravity of a central source are conic sections: the shapes of the curves of intersection between a plane and a cone.

A small crater has incised a short section along the northern rim. The interior of this floor-fractured crater is notable for the curving ridge that parallels the northwestern inner wall. The remainder of this circular form can be traced out across the interior by an intermittent pattern of lower-albedo surface that is concentric with the inner wall. There are also several rilles marking the interior surface, particularly along the outer edges.

In an annular drainage pattern streams traces a tangential or greater concentric path along a belt of weak rock so, with others, a roughly traced out ring can be seen. It is best displayed by streams draining a maturely dissected structural dome or basin where erosion has exposed rimming sedimentary strata of greatly varying degrees of hardness, as in the Red Valley, which nearly encircles the domal structure of the Black Hills of South Dakota.

During the year 2006-2007 about 200 cases were referred to CIA for investigation. Out of which 126 cases have been traced out. They worked out 11 cases of kidnapping and 09 miscellaneous cases. The wing has developed over the years specialized skills to trace out the gangs and criminals behind the heinous crimes as they incessantly keep on diligently working and tracing out the links of criminal gangs with various types of crimes.

The game is played on a sheet of graph paper, with any set of designs traced out. It is most commonly played on rectangular board like a 6×6 square or a checkerboard, but it can also be played on an entirely irregular polygon or a cylindrical board. Two players have a collection of dominoes which they place on the grid in turn. A player can place a domino either horizontally or vertically.

In 3D microfabrication, a block of gel containing monomers and a 2-photon active photoinitiator is prepared as a raw material. Application of a focused laser to the block results in polymerization only at the focal spot of the laser, where the intensity of the absorbed light is highest. The shape of an object can therefore be traced out by the laser, and then the excess gel can be washed away to leave the traced solid.

In a rotating or orbiting object, there is a relation between distance from the axis, r, tangential speed,v, and the angular frequency of the rotation. During one period, T, a body in circular motion travels a distance vT. This distance is also equal to the circumference of the path traced out by the body, 2\pi r. Setting these two quantities equal, and recalling the link between period and angular frequency we obtain: \omega = v/r.

Lieutenant Joseph Gilbert Totten of the U.S. Engineers traced out the position of the proposed fortifications. Van Rensselaer appointed Lieutenant Colonel Winfield Scott of the 2nd U.S. Artillery to take command of the regulars on Queenston Heights. Brigadier General William Wadsworth, who was nominally present as a volunteer and who waived his right to overall command, took charge of the militia. There were few complete formed units; there was only a collection of unorganised detachments, some without their officers.

Both he and his wife Belle were Spiritualists, and the couple decided to consult the spirits for guidance. Using a planchette, a device similar to a Ouija board, they traced out the message :Mark Wyman take the Bradbury building and you will be... Successful. Mark Wyman was George's younger brother, who had died at the age of 8. At first, they had trouble reading the final word, as it was written upside down in relation to the rest of the message.

According to the local residents, it is said that the origin of water is difficult to be traced out since an underground stream surfaces here. There used to be a 240 meter long canopy rope walk, about 35 to 40 feet in height . There are number of trek routes in different categories of difficulty, giving an option for the visitor to choose their route. In the area there is an ancient Siva temple which is flooded with devotees during Sivarathri festival.

CIA is the investigation wing of Islamabad Capital Territory Police working under supervision of an SP. It is responsible for tracing out heinous cases referred to it by SSP Islamabad. Its office is located at I-9 Markaz and presently DSP Bashir Noon is heading the wing with 70 officers. Many high-profile and important cases have been traced out by DSP Bashir Noon. He is known for his professional expertise and without doubt is an asset to the department.

In many ways Nell's approach goes back to Francois Quesnay; where money traced out the transactions between the different classes and sectors of society. Although Wassily Leontief was best known for his 'Input Output Mode', a major contribution to economic analysis could be found in his doctoral thesis, done in 1928 at the University of Berlin, on 'Economics as a Circulation' (in German "Wirtschaft als Kreislauf."), under the direction of L.Von Bortkiewicz and Werner Sombart. This work helped to influence Nell's vision of 'Monetary Circulation'.

One of the major factor that affects the flora and fauna of the earth is the change of climate at the local, regional and global scale. These changes are preserved over the period of time as a fossil record and through paleolimnological methods, these changes can be traced out and also helpful for the prediction of the future climate change. Chironomids are one of the best indicators of climate change. These are two winged flies that belong to the family Chironomidae with 500 to 15,000 species.

A presidio was established as a sub prefecture of the district of Tolimán. The official foundation ceremony included a mass officiated by Friar Tomas Aquino Ramirez de Prado, and declared as the Villa de Peña Millera de la Santisima Virgen de la Asunción. The new settlement was traced out with a plaza, a church, monastery cemetery and gardens on the north side with lands partitioned out on the other sides. In addition, four official pasturelands for cattle were marked off in each of the cardinal directions.

The line is operated by a single 0-4-2 steam-outline diesel locomotive. The line today does not follow any of the former trackbed of the Waterloo Mining Railroad. The original line began below at the mouth of Wall Street Canyon, and is now a paved road for tourists to access Calico from Interstate 10. Some segments of the old railbed can still be traced out in some places in the desert, but much has now been covered by housing developments of Yermo.

One player at a time stands at the centre of the Circle of Cash, a large circle of lights traced out on the stage floor. The money is placed on the Circle and begins to orbit the player. Three spots are marked as tunnels, which can randomly allow the money to pass through or reverse its direction; these tunnels are located directly behind the player and to his/her left and right. A buzzer known as the Bang Button is on a pedestal before the player.

The areas where this relief is created no longer repel the electrons from the flood gun which now pass through the mesh and illuminate the phosphor screen. Consequently, the image that was briefly traced out by the main gun continues to be displayed after it has occurred. The image can be 'erased' by resupplying the external voltage to the mesh restoring its constant potential. The time for which the image can be displayed was limited because, in practice, the flood gun slowly neutralises the charge on the storage mesh.

0 dearest Mother, enlighten my understanding, that I may avoid all errors and sins, that I may walk with courage in the paths traced out for me by you and your Son. Amen. The Memorare of Our Lady of La Salette is as follows: :Remember, Our Lady of La Salette, true Mother of Sorrows, the tears you shed for us on Calvary. Remember also the care you have taken to keep us faithful to Christ, your Son. Having done so much for your children, you will not now abandon us.

By the early 20th century massive deforestation was causing problems such as desertification, erosion, flooding from unimpeded runoff and more. Quevedo was the director of public works of Mexico City in the early 20th century and designed the roads extending Colonia Condesa and Colonia Roma, so that they would be wide and lined with trees, minimizing the loss of green space. He also traced out Avenida Insurgentes. In 1904, he founded the Junta Central de Bosques y Arbolados (Central Committee of Forests and Tree Areas), which was the first environmental protection institution in Mexico.

Making a wayang kulit figure that is suitable for a performance involves hand work that takes several weeks, with the artists working together in groups. They start from master models (typically on paper) which are traced out onto skin or parchment, providing the figures with an outline and with indications of any holes that will need to be cut (such as for the mouth or eyes). The figures are then smoothed, usually with a glass bottle, and primed. The structure is inspected and eventually the details are worked through.

The gatehouse of Thornton Abbey from the outside Gatehouse of Thornton Abbey from the inside The founding abbey building from the 12th century was Romanesque in style, but nothing of it remains above ground. The later abbey from the 13th/14th centuries was built in Early Gothic style. Little remains of the building, except for three walls of the chapter house and part of the cloister, though the ground plan of the abbey is traced out. The main interest lies in the gatehouse which is amongst the earliest large-scale uses of brick in England.

Saxony opposed the project because the projected stations would have been located too far from the populated places in the Schweinitz valley, and the building costs were regarded as too high. Nevertheless, on 13 August 1913 the Royal Saxon State Railways consented to a concession for a standard gauge line from Olbernhau to Deutschneudorf, which was to be traced out as a secondary line, but with the parameters of a main line because of the expected through traffic to Bohemia. Thus, there were no level crossings at all on the whole line.

Its disk of stars can be traced out to a radius of around . This disk begins to warp at a radius of around , suggesting the perturbing effect of in-falling matter from the surrounding medium. The rotational behavior of the galaxy suggests there is a massive nuclear bulge, with a low-ionization nuclear emission-line region (LINER) at the core; a type of region that is characterized by spectral line emission from weakly ionized atoms. A prominent molecular ring is orbiting at a radius of , which is providing a star-forming region of gas and dust.

This direct connection between linkages and algebraic curves was recently named the Kempe's universality theoremA. Saxena (2011) Kempe’s Linkages and the Universality Theorem , RESONANCE that any bounded subset of an algebraic curve may be traced out by the motion of one of the joints in a suitably chosen linkage. Kempe's proof was flawed, and the first complete proof was provided in 2002, based on his ideas.M. Kapovich and J. J. Millson (2002), Universality theorems for configguration spaces of planar linkages Topology, Pergamon Press.. In 1877 Kempe discovered new straight line linkages and published his influential lectures on the subject.

A circle is a shape consisting of all points in a plane that are a given distance from a given point, the centre; equivalently it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant. The distance between any point of the circle and the centre is called the radius. This article is about circles in Euclidean geometry, and, in particular, the Euclidean plane, except where otherwise noted. Specifically, a circle is a simple closed curve that divides the plane into two regions: an interior and an exterior.

It may be helpful to visualize this situation using spacetime diagrams. For a given observer, the t-axis is defined to be a point traced out in time by the origin of the spatial coordinate x, and is drawn vertically. The x-axis is defined as the set of all points in space at the time t = 0, and is drawn horizontally. The statement that the speed of light is the same for all observers is represented by drawing a light ray as a 45° line, regardless of the speed of the source relative to the speed of the observer.

In addition to Offertories and Communions the two volume Venetian publication contains over a dozen other pieces, such as hymns, antiphons, a magnificat, and even three instrumental fantasias. In his compositions Zieleński relies on his own creative invention and does not, in general, make use of the cantus firmi. The few pre-existing melodies which may be traced out in his pieces are based not on plainsong but on the melodies of Polish songs. The sets consist of large-scale double- and triple-choir antiphons, as well as some monodic works typical of the Seconda pratica style of early Monteverdi.

In 2000, Marco Machacuay (the chief of excavations at the time) and his colleague, Rocío Aramburú, discovered a large shape etched on the ground in circular stone lines near Caral. This image, known as a geoglyph, is located on the desert floor just west of the main site at Caral. When traced out, the lines form the design of a human face with long, streaming hair and a gaping mouth. This geoglyph is similar to the screaming, bleeding figures found etched onto the stone walls at a site called Cerro Sechín, in the Casma Valley to the north.

This policy resulted in a substantial shrinkage of the Romanian population in the province. By 1941, out of 250,000 Romanians in Northern Bukovina, only 192,000 were left. The territory of the Moldavian SSR was composed of Bessarabia (except for Southern Bessarabia, assigned to Ukraine) and a part of the territory of the former Moldavian Autonomous Soviet Socialist Republic (Transnistria), founded in 1924 within the territory of Ukraine. In the document confirming the establishment of the Moldavian Autonomous Soviet Socialist Republic (MASSR) of 12 October 1924 the West frontier of the republic was traced out not along the Dniester River but the Prut River.

The Crowsnest Highway is an east-west highway in British Columbia and Alberta, Canada. It stretches across the southern portions of both provinces, from Hope, British Columbia to Medicine Hat, Alberta, providing the shortest highway connection between the Lower Mainland and southeast Alberta through the Canadian Rockies. The mostly two-lane highway was officially designated in 1932, mainly following a mid-19th-century gold rush trail originally traced out by an engineer named Edgar Dewdney. It takes its name from the Crowsnest Pass, the location at which the highway crosses the Continental Divide between British Columbia and Alberta.

In type II string theory, one considers surfaces traced out by strings as they travel along paths in a Calabi–Yau 3-fold. Following the path integral formulation of quantum mechanics, one wishes to compute certain integrals over the space of all such surfaces. Because such a space is infinite-dimensional, these path integrals are not mathematically well-defined in general. However, under the A-twist one can deduce that the surfaces are parametrized by pseudoholomorphic curves, and so the path integrals reduce to integrals over moduli spaces of pseudoholomorphic curves (or rather stable maps), which are finite-dimensional.

According to Campbell, his family history had been traced out, despite their differing views about the Spanish Civil War, by, "that valiant and fine writer, my friend, the late George Orwell." Campbell (1952), page 4. Campbell's paternal ancestors were Scottish Covenanters and members of Clan Campbell, who left the Gàidhealtachd of Scotland after their Chief, the Earl of Argyll, was defeated in battle by the Royalist Marquess of Montrose in 1645. The Campbell family then settled as part of the Plantation of Ulster at Carndonagh, in Inishowen, County Donegal.Pearce (2004), page 4. Campbell (1952), page 3.

Philip of Dreux, the famed crusader bishop of Beauvais, wished to found a convent of the Cistercian order. In 1217 he set aside an orchard southwest of Beauvais, on which were traced out the plans for construction, as well as seven arpents (6-7 acres) of vines. Philip died before the project was completed and his successor, Bishop Milo of Nanteuil, raised the rest of the funds, and it was completed in 1218. Pope Gregory IX issued a bull from the Lateran Palace on the 8 June 1230 which sanctioned the new abbey and declared the funds raised for its endowment protected.

The straight skeleton of a polygon is defined by a continuous shrinking process in which the edges of the polygon are moved inwards parallel to themselves at a constant speed. As the edges move in this way, the vertices where pairs of edges meet also move, at speeds that depend on the angle of the vertex. If one of these moving vertices collides with a nonadjacent edge, the polygon is split in two by the collision, and the process continues in each part. The straight skeleton is the set of curves traced out by the moving vertices in this process.

A herpolhode is the curve traced out by the endpoint of the angular velocity vector ω of a rigid rotor, a rotating rigid body. The endpoint of the angular velocity moves in a plane in absolute space, called the invariable plane, that is orthogonal to the angular momentum vector L. The fact that the herpolhode is a curve in the invariable plane appears as part of Poinsot's construction. The trajectory of the angular velocity around the angular momentum in the invariable plane is a circle in the case of a symmetric top, but in the general case wiggles inside an annulus, while still being concave towards the angular momentum.

In 1876 Alfred B. Kempe published his article On a General Method of describing Plane Curves of the nth degree by Linkwork, which showed that for an arbitrary algebraic plane curve a linkage can be constructed that draws the curve. This direct connection between linkages and algebraic curves has been named Kempe's universality theoremA. Saxena (2011) Kempe’s Linkages and the Universality Theorem , RESONANCE that any bounded subset of an algebraic curve may be traced out by the motion of one of the joints in a suitably chosen linkage. Kempe's proof was flawed and the first complete proof was provided in 2002 based on his ideas.

Newton's idea of a centripetal force corresponds to what is nowadays referred to as a central force. When a satellite is in orbit around a planet, gravity is considered to be a centripetal force even though in the case of eccentric orbits, the gravitational force is directed towards the focus, and not towards the instantaneous center of curvature. Another example of centripetal force arises in the helix that is traced out when a charged particle moves in a uniform magnetic field in the absence of other external forces. In this case, the magnetic force is the centripetal force that acts towards the helix axis.

Immediately they rushed to the guard of the train and complained about the incident, which triggered in the search of the track by some young men of the locality, and the Gang-man of the Vallathol Nagar Railway Station. All of them engaged in a search at the railway track, and ultimately, by about 9.30 p.m., the distorted and mutilated body of the deceased which was in almost naked state could be traced out from the side of the railway track wherein she was subjected to rape. The deceased was seen fighting for her life and was seen moving her right hand and right leg.

Therefore, as two color charges are separated, at some point it becomes energetically favorable for a new quark–antiquark pair to appear, rather than extending the tube further. As a result of this, when quarks are produced in particle accelerators, instead of seeing the individual quarks in detectors, scientists see "jets" of many color-neutral particles (mesons and baryons), clustered together. This process is called hadronization, fragmentation, or string breaking. The confining phase is usually defined by the behavior of the action of the Wilson loop, which is simply the path in spacetime traced out by a quark–antiquark pair created at one point and annihilated at another point.

This monotonicity cannot happen for a simple closed curve (by the four- vertex theorem, there are at least four vertices where the curvature reaches an extreme point) but for such curves the theorem can be applied to the arcs of the curves between its vertices. The theorem is named after Peter Tait, who published it in 1896, and Adolf Kneser, who rediscovered it and published it in 1912. Tait's proof follows simply from the properties of the evolute, the curve traced out by the centers of osculating circles. For curves with monotone curvature, the arc length along the evolute between two centers equals the difference in radii of the corresponding circles.

The Roman physician Galen also argued for the importance of the brain, and theorized in some depth about how it might work. Galen traced out the anatomical relationships among brain, nerves, and muscles, demonstrating that all muscles in the body are connected to the brain through a branching network of nerves. He postulated that nerves activate muscles mechanically by carrying a mysterious substance he called pneumata psychikon, usually translated as "animal spirits". Galen's ideas were widely known during the Middle Ages, but not much further progress came until the Renaissance, when detailed anatomical study resumed, combined with the theoretical speculations of René Descartes and those who followed him.

In these models the phase paths can "spiral in" towards zero, "spiral out" towards infinity, or reach neutrally stable situations called centres where the path traced out can be either circular, elliptical, or ovoid, or some variant thereof. This is useful in determining if the dynamics are stable or not. Other examples of oscillatory systems are certain chemical reactions with multiple steps, some of which involve dynamic equilibria rather than reactions that go to completion. In such cases one can model the rise and fall of reactant and product concentration (or mass, or amount of substance) with the correct differential equations and a good understanding of chemical kinetics.

A cycloid (a common trochoid) generated by a rolling circle In geometry, a trochoid (from the Greek word for wheel, "trochos") is a roulette formed by a circle rolling along a line. In other words, it is the curve traced out by a point fixed to a circle (where the point may be on, inside, or outside the circle) as it rolls along a straight line. If the point is on the circle, the trochoid is called common (also known as a cycloid); if the point is inside the circle, the trochoid is curtate; and if the point is outside the circle, the trochoid is prolate. The word "trochoid" was coined by Gilles de Roberval.

Close-up of banded iron formation specimen from Upper Michigan Banded iron formations of the Great Lakes region and the Frere Formation of western Australia are somewhat different in character and are sometimes described as granular iron formations or GIFs. Their iron sediments are granular to oolitic in character, forming discrete grains about a millimeter in diameter, and they lack microbanding in their chert mesobands. They also show more irregular mesobanding, with indications of ripples and other sedimentary structures, and their mesobands cannot be traced out any great distance. Though they form well-defined, discrete units, these are commonly interbedded with coarse to medium-grained epiclastic sediments (sediments formed by weathering of rock).

For more precise and visually decorative engravings, a laser table (also known as an "X–Y" or "XY" table) is used. The laser is usually fixed permanently to the side of the table and emits light towards a pair of movable mirrors so that every point of the table surface can be swept by the laser. At the point of engraving, the laser beam is focused through a lens at the engraving surface, allowing very precise and intricate patterns to be traced out. A typical setup of a laser table involves the fixed laser emitting light parallel to one axis of the table aimed at a mirror mounted on the end of an adjustable rail.

Among aquatic invertebrates, different families of aquatic fly larvae can be traced out in the lake sediments of Quaternary era. Among them, Chironomids are of greatest ecological importance due to their diverse habitat in the aquatic ecosystem, feeding habitat, important component in the food web and above all their usage as a plaeolimnological studies because their head capsule and feeding structures are fossilized in the lake sediments. Chironomids complete their larval stage in the water and its life cycle continues up to several years while adult life span is very short. They have an important role in the degradation of material in the aquatic ecosystem and serve as an important part of the food web during their whole life cycle.

According to the U.S. Weather Bureau, the "followed an average course for the type of August hurricanes that pass through the Yucatán Channel", but maintained an unusually brisk forward speed throughout its life. A possible precursor disturbance may have originated as early as August 8 near Africa, but observations were inconclusive in determining the formation of a tropical cyclone. The hurricane was first definitively detected as a tropical storm east of Barbados on August 12, based on a 40-mph (64 km/h) wind measurement from a nearby ship. There were no other observations of similarly gusty winds or low air pressures over the next three days while the system traced out the southern periphery of the Azores High westward into the eastern Caribbean Sea.

Figure 5: Crossing a rotating carousel walking at constant speed from the center of the carousel to its edge, a spiral is traced out in the inertial frame, while a simple straight radial path is seen in the frame of the carousel. Figure 5 shows another example comparing the observations of an inertial observer with those of an observer on a rotating carousel.For a similar example, see , and The carousel rotates at a constant angular velocity represented by the vector Ω with magnitude ω, pointing upward according to the right-hand rule. A rider on the carousel walks radially across it at constant speed, in what appears to the walker to be the straight line path inclined at 45° in Figure 5.

The definitions and results in this section are taken from the 1913 text, Plane and Solid Geometry by George Wentworth and David Eugene Smith . A ' is a surface consisting of all the points on all the lines which are parallel to a given line and which pass through a fixed plane curve in a plane not parallel to the given line. Any line in this family of parallel lines is called an element of the cylindrical surface. From a kinematics point of view, given a plane curve, called the directrix, a cylindrical surface is that surface traced out by a line, called the generatrix, not in the plane of the directrix, moving parallel to itself and always passing through the directrix.

Philosophers were less concerned with such mathematical calculations than with the nature of the celestial spheres, their relation to revealed accounts of created nature, and the causes of their motion. Adi Setia describes the debate among Islamic scholars in the twelfth century, based on the commentary of Fakhr al-Din al-Razi about whether the celestial spheres are real, concrete physical bodies or "merely the abstract circles in the heavens traced out… by the various stars and planets." Setia points out that most of the learned, and the astronomers, said they were solid spheres "on which the stars turn… and this view is closer to the apparent sense of the Qur'anic verses regarding the celestial orbits." However, al-Razi mentions that some, such as the Islamic scholar Dahhak, considered them to be abstract.

We can verify that g is a single-valued function on this surface by tracing a circuit around a circle of unit radius centered at . Commencing at the point on the first sheet we turn halfway around the circle before encountering the cut at . The cut forces us onto the second sheet, so that when z has traced out one full turn around the branch point , w has taken just one-half of a full turn, the sign of w has been reversed (since ), and our path has taken us to the point on the second sheet of the surface. Continuing on through another half turn we encounter the other side of the cut, where , and finally reach our starting point ( on the first sheet) after making two full turns around the branch point.

Its central geometric object is a lightsheet, defined as a region traced out by non-expanding light-rays emitted orthogonally from an arbitrary surface B. For example, if B is a sphere at a moment of time in Minkowski space, then there are two lightsheets, generated by the past or future directed light-rays emitted towards the interior of the sphere at that time. If B is a sphere surrounding a large region in an expanding universe (an anti-trapped sphere), then there are again two light-sheets that can be considered. Both are directed towards the past, to the interior or the exterior. If B is a trapped surface, such as the surface of a star in its final stages of gravitational collapse, then the lightsheets are directed to the future.

The most commonly used cam is the cam plate (also known as disc cam or radial cam) which is cut out of a piece of flat metal or plate. Here, the follower moves in a plane perpendicular to the axis of rotation of the camshaft.Introduction to Mechanisms - Cams "The follower moves in a plane perpendicular to the axis of rotation of the camshaft." Several key terms are relevant in such a construction of plate cams: base circle, prime circle (with radius equal to the sum of the follower radius and the base circle radius), pitch curve which is the radial curve traced out by applying the radial displacements away from the prime circle across all angles, and the lobe separation angle (LSA - the angle between two adjacent intake and exhaust cam lobes).

Victorian Eel Fishery – Management Plan Accessed 25 November 2008 Near Lake Bolac a semi-permanent village extended some 35 kilometres along the river bank during autumn. George Augustus Robinson on 7 July 1841 described some of the infrastructure that had been constructed near Mount William: > ...an area of at least 15 acres was thus traced out ... These works must > have been executed at great cost of labour ... There must have been some > thousands of yards of this trenching and banking. The whole of the water > from the mountain rivulets is made to pass through this trenching ere it > reaches the marsh ...Harry Lourandos, pp. 63–65, Continent of Hunter- > gatherers: New Perspectives in Australian Prehistory, Cambridge University > Press, 1997, The way of life of the Aboriginal people of Western Victoria, who included the Gunditjmara, differed from other groups in Victoria in several respects.

Near Mount William, an elaborate network of channels, weirs and eel traps and stone shelters had been constructed, indicative of a semi-permanent lifestyle in which eels were an important economic component for food and bartering, particularly the Short-finned eel. Near Lake Bolac a semi-permanent village extended some along the river bank during autumn. George Augustus Robinson on 7 July 1841 described some of the infrastructure that had been constructed near Mount William: :'...an area of at least was thus traced out... These works must have been executed at great cost of labour... There must have been some thousands of yards of this trenching and banking. The whole of the water from the mountain rivulets is made to pass through this trenching ere it reaches the marsh...' In mid summer, gatherings for ceremony and hunting took place at Mirraewuae, a marsh near Hexham rich with emu and other game.

Chapter 34 The typical way to consider polarization is to keep track of the orientation of the electric field vector as the electromagnetic wave propagates. The electric field vector of a plane wave may be arbitrarily divided into two perpendicular components labeled x and y (with z indicating the direction of travel). The shape traced out in the x-y plane by the electric field vector is a Lissajous figure that describes the polarization state. The following figures show some examples of the evolution of the electric field vector (blue), with time (the vertical axes), at a particular point in space, along with its x and y components (red/left and green/right), and the path traced by the vector in the plane (purple): The same evolution would occur when looking at the electric field at a particular time while evolving the point in space, along the direction opposite to propagation.

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 .

Messier 49 (also known as M 49 or NGC 4472) is an elliptical galaxy located about away in the equatorial constellation of Virgo. This galaxy was discovered by French astronomer Charles Messier on February 16, 1777. As an elliptical galaxy, Messier 49 has the physical form of a radio galaxy, but it only has the radio emission of a normal galaxy. From the detected radio emission, the core region has roughly 1053 erg (1046 J or 1022 YJ) of synchrotron energy. The nucleus of this galaxy is emitting X-rays, suggesting the likely presence of a supermassive black hole with an estimated mass of , or 565 million times the mass of the Sun. X-ray emissions shows a structure to the north of Messier 49 that resembles a bow shock. To the southwest of the core, the luminous outline of the galaxy can be traced out to a distance of 260 kpc. The only supernova event observed within this galaxy is SN 1969Q, discovered in June 1969.

There were several causes of the deflation of the severe depression of 1839–43, which included an oversupply of agricultural commodities (importantly cotton) as new cropland came into production following large federal land sales a few years earlier, banks requiring payment in gold or silver, the failure of several banks, default by several states on their bonds and British banks cutting back on specie flow to the U.S. This cycle has been traced out on the broad scale during the Great Depression. Partly because of overcapacity and market saturation and partly as a result of the Smoot-Hawley Tariff Act, international trade contracted sharply, severely reducing demand for goods, thereby idling a great deal of capacity, and setting off a string of bank failures. A similar situation in Japan, beginning with the stock and real estate market collapse in the early 1990s, was arrested by the Japanese government preventing the collapse of most banks and taking over direct control of several in the worst condition.

" Ibn al-Haytham, in his Book of Optics (1021), was also the first to discover that the celestial spheres do not consist of solid matter, and he also discovered that the heavens are less dense than the air. These views were later repeated by Witelo and had a significant influence on the Copernican and Tychonic systems of astronomy. In the 12th century, Fakhr al-Din al-Razi participated in the debate among Islamic scholars over whether the celestial spheres or orbits (falak) are "to be considered as real, concrete physical bodies" or "merely the abstract circles in the heavens traced out year in and year out by the various stars and planets." He points out that many astronomers prefer to see them as solid spheres "on which the stars turn," while others, such as the Islamic scholar Dahhak, view the celestial sphere as "not a body but merely the abstract orbit traced by the stars.

Al Anbar Provincial Security Force 2, Iraqi Army demolition experts and U.S. Soldiers from 3rd Battalion, 69th Armor Regiment, 1st Brigade Combat Team, 3rd Infantry Division, Task Force Pathfinder (with elements from the 321st Engineer Battalion and C company 397th Engineer company) conducted the weeks long clearing operation, targeting one of the remaining hotspots in the brigade’s area of operations. TF Pathfinder spent long hours conducting route clearance, often on mission for more than 24 hours at a time, clearing IED threats so that Provincial Security Force 2 could complete their mission. Operation Forsythe Park started in the early morning hours of 26 April with multiple Coalition Soldiers being injured in the opening minutes of the Operation by IED's that had been emplaced in strategic areas such as land bridges over canals, with command executed detonations. One such firing point was traced out at over 600 meters and had to be dug out with a pick.

Love :had a compass whose whirling dance traced out a :sphere of love in the void: in the center thereof :rose a fountain.From towards the end of the "Morning" section Over the years following the composition of Circus of the Sun, Lax's poetry became more and more stripped down to essentials, concentrating on simplicity and making the most out of the fewest components, a technique common to artistic minimalism. Sometimes these pieces consisted of single words, even single syllables, running page after page. As a consequence his work was perceived as sharing the characteristics of Concrete poetry and was included in Stephen Bann’s defining Poetry: An International Anthology (1967) and mentioned in Mary Ellen Solt’s study, Concrete Poetry: A World View (1968).Chapter 18, "United States", Ubu Web Lax certainly shared an interest in artistic procedures with his friend Ad Reinhardt and reflected that artist’s series of black paintings in his own "Homage to Reinhardt": ::black/black/black// ::blue/blue/blue// ::black/black/black/black// ::blue/blue/blueJack Kalmitz,Views, Seawall Press 2012, pp.