单词 | Descartes Circle Theorem |
释义 | Descartes Circle TheoremA special case of Apollonius' Problem requiring the determination of a Circle touching three mutually tangentCircles (also called the Kissing Circles Problem). There are two solutions: a small circlesurrounded by the three original Circles, and a large circle surrounding the original three. FrederickSoddy gave the Formula for finding the Radius of the so-called inner and outer Soddy Circles given theRadii of the other three. The relationship is ![]() where ![]() ![]() ![]() ![]() ![]() ![]() See also Apollonius' Problem, Four Coins Problem, Soddy Circles, Sphere Packing
Boyer, C. B. and Merzbach, U. C. A History of Mathematics, 2nd ed. New York: Wiley, 1991. Coxeter, H. S. M. Introduction to Geometry, 2nd ed. New York: Wiley, pp. 13-16, 1969. Wilker, J. B. ``Four Proofs of a Generalization of the Descartes Circle Theorem.'' Amer. Math. Monthly 76, 278-282, 1969. |
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