For example he shows how to deform a circle into an ellipse and proves other results on deforming conic sections. |
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He showed that in any hexagon formed of six tangents to a conic, the three diagonals meet at a point. |
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Many eighteenth-century manuals on gauging treated barrels as solids generated by rotating conic sections about their axes. |
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In 1865 he submitted his doctoral dissertation on a new method to determine the characteristics of conic systems to the University of Copenhagen. |
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Conic aspheres can also be tested with spherical wavefronts at their conic conjugate points. |
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The device looks like a conic bulb, which is connected to a discharge pump. |
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If all the vertices of a hexagon lie on a conic, and if the opposite sides intersect, then the points of intersection lie on a line. |
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He worked on conic sections and produced important theorems in projective geometry. |
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The dorsal conic spine-like structures could be a homology of cuticular spicules of polyplacophorans and aplacophorans. |
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Omar Khayyam gave a complete classification of cubic equations with geometric solutions found by means of intersecting conic sections. |
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The Steiner theorem states that the two pencils by which a conic is projected from two of its points are projectively related. |
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These three trajectories are known as conic sections, as they are also the curves produced by cutting a cone along different planes. |
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Sturm's theoretical work in mathematical physics involved the study of caustic curves, and poles and polars of conic sections. |
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It's the other conic sections that confuse me, like ellipses and hyperbolas. |
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First we should note that conic sections to Apollonius are by definition the curves formed when a plane intersects the surface of a cone. |
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Modernism is assumed to be a series of separate known conic elements and glittering remains. |
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He developed the hemicyclium, a sundial which has the hour lines drawn on the surface of a conic section giving greater accuracy. |
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Cavalieri also wrote on conic sections, trigonometry, optics, astronomy, and astrology. |
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The first students of conic sections, and possibly Theaetetus, the creator of solid geometry, were members of the Academy. |
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If four of the points are collinear, or two of the points coincide, no conic is created. |
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Suitable for: conic drives, drives with belt-shifters, chippers, crushers, paper mills, etc. Suitable for cross drives. |
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As an urban design gesture it works as large, slow tempo pedal notes, allowing the refurbished stables to act as an conic flourish on Macquarie Street. |
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You can do constructions with points, vectors, segments, lines, conic sections as well as functions and change them dynamically afterwards. |
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Catching it temporarily gives you the ability to capture alien ships with a conic beam much in the same way that the aliens could capture your ship in the old arcade game. |
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How this connects up to conventional conic orbits is not entirely clear. |
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Built on water in the Tokyo bay, its conic shape would remind that of Mount Fuji-Yama. |
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The conic shape of the eight small cyclones around the top of each vacuum creates a dramatic shape, but they are in place to serve a purpose first. |
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Section connection is effected by means of assembling conic stirrups and water proofing is granted by gaskets. |
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In many cases, the result is that the edge of the source is imaged to the edge of the receiver, and the reflector profile that performs the mapping is an off-axis conic. |
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The stem presents two conic shape figures and a oval sphere. |
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The endosperm cap was placed on the needle and was pierced by moving the needle down into a polyvinyl chloride block with a conic hole with a minimum diameter of 0.7 mm. |
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The conic hand is usually medium sized and the palm is slightly tapering. |
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An intern conic jet deflector is hold in the internal dented bottom by beams in profiled welded on edge in order to avoid the product retention. |
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Although it covers topics in orbital motion, planetary motion, conservation of energy, conic sections and vectors, it is not meant to be a definitive treatment of these topics. |
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To better recover these substances and improve the quality of this water, most of the 300 flat bottom tanks were replaced by conic bottom tanks, which improve product flow. |
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A parameter that specifies the shape of a conic section. |
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Decide on the conic section that you would like to make. |
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Conic perspective, specific command that produces a perspective point of view by interactively positioning a camera point and a target point to create a conic perspective view, recoverable with the view control command. |
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Insert the cable into the counterweight, from the conic part, turning it. |
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Slice them any way you like, and you have a real-world example of conic sections 6 which can take the form of an ellipse, parabola, or hyperbola. |
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An example of the use of the rectifying latitude is the Equidistant conic projection. |
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The parameter of the principal axis of a conic section is called the latus rectum. |
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Students can graph conic sections, then determine and display their characteristics. |
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Current optical design of optical instruments is based on conic or aspheric surfaces of revolution. |
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The topics include functions, trigonomic functions, polar coordinates and parametric equations, conic sections, and sequences and series. |
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The fifth edition adds optional sections on parametric graphing, arc length, and parametric equations for conic sections. |
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Following his lead, Pascal made his surprising discovery that the intersections of the three pairs of opposite sides of a hexagon inscribed in a conic lie on a straight line. |
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He followed the way opened by al-Hasan ibn Musa, particularly in his work on the measure of curved planes and solids, and on the properties of conic sections. |
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He argued that a mirror shaped like the part of a conic section, would correct the spherical aberration that flawed the accuracy of refracting telescopes. |
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Gauss-Kruger and versions of Lambert Conformable Conic and Oblique Mercator map projections have been added. |
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