单词 | Conic Section |
释义 | Conic Section![]() The conic sections are the nondegenerate curves generated by the intersections of a Plane with one or twoNappes of a Cone. For a Plane parallel to a Cross-Section, a Circle isproduced. The closed curve produced by the intersection of a single Nappe with an inclined Plane is anEllipse or Parabola. The curve produced by a Plane intersecting both Nappes is aHyperbola. The Ellipse and Hyperbola are known as Central Conics. Because of this simple geometric interpretation, the conic sections were studied by the Greeks long before their applicationto inverse square law orbits was known. Apollonius A conic section may more formally be defined as the locus of a point ![]() If ![]() ![]() ![]() In standard form, a conic section is written ![]() where ![]() ![]()
Besant, W. H. Conic Sections, Treated Geometrically, 8th ed. rev. Cambridge, England: Deighton, Bell, 1890. Casey, J. ``Special Relations of Conic Sections'' and ``Invariant Theory of Conics.'' Chs. 9 and 15 in A Treatise on the Analytical Geometry of the Point, Line, Circle, and Conic Sections, Containing an Account of Its Most Recent Extensions, with Numerous Examples, 2nd ed., rev. enl. Dublin: Hodges, Figgis, & Co., pp. 307-332 and 462-545, 1893. Coolidge, J. L. A History of the Conic Sections and Quadric Surfaces. New York: Dover, 1968. Coxeter, H. S. M. and Greitzer, S. L. Geometry Revisited. Washington, DC: Math. Assoc. Amer., pp. 138-141, 1967. Downs, J. W. Conic Sections. Dale Seymour Pub., 1993. Iyanaga, S. and Kawada, Y. (Eds.). ``Conic Sections.'' §80 in Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, pp. 271-276, 1980. Le Lionnais, F. Les nombres remarquables. Paris: Hermann, p. 56, 1983. Lee, X. ``Conic Sections.''http://www.best.com/~xah/SpecialPlaneCurves_dir/ConicSections_dir/conicSections.html Ogilvy, C. S. ``The Conic Sections.'' Ch. 6 in Excursions in Geometry. New York: Dover, pp. 73-85, 1990. Pappas, T. ``Conic Sections.'' The Joy of Mathematics. San Carlos, CA: Wide World Publ./Tetra, pp. 196-197, 1989. Salmon, G. Conic Sections, 6th ed. New York: Chelsea, 1954. Smith, C. Geometric Conics. London: MacMillan, 1894. Sommerville, D. M. Y. Analytical Conics, 3rd ed. London: G. Bell and Sons, 1961. Yates, R. C. ``Conics.'' A Handbook on Curves and Their Properties. Ann Arbor, MI: J. W. Edwards, pp. 36-56, 1952. |
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