A Straightforward Proof of Descartes’s Circle Theorem
- 25 Downloads
There are probably not many formulas in mathematics in the discovery of which a princess was instrumental and that are described in a poem written by a Nobel laureate (in Chemistry!). Yet such is the case for what is now known as Descartes’s circle formula.
I want to thank Damaris Schindler, of Utrecht University, for bringing me back to this old favorite of mine.
- Lambert, J. H. Deutscher gelehrter Briefwechsel, Band I. Berlin, 1781.Google Scholar
- Coxeter, H. S. M. The Problem of Apollonius. Amer. Math. Monthly 75:1 (1968), 5–15.Google Scholar
- Coxeter, H. S. M. Loxodromic Sequences of Tangent Spheres. Aequationes Math. 1 (1968), 104–121.Google Scholar
- Descartes, R. Oeuvres. Published by Ch. Adam and Paul Tannery; Correspondance, Vol. IV (July 1643 to April 1647). Paris, Léopold Cerf, 1901, pp. 37, 49.Google Scholar
- Shapiro, L. The Correspondence between Princess Elisabeth of Bohemia and René Descartes. University of Chicago Press, Chicago, 2007.Google Scholar
- Soddy, F. The Kiss Precise. Nature 137 (1936), 1021.Google Scholar
- Nature 139 (1937), 62.Google Scholar
- Lagarias, J. C., Mallows, C. L., and Wilks A. R. Beyond the Descartes Circle Theorem. Amer. Math. Monthly 109:4 (2002), 338–361.Google Scholar
- Steiner, J. Fortsetzung der geometrischen Betrachtungen, J. Reine Angew. Math. 1 (1826), 252–288.Google Scholar
- Pedoe, D. On a Theorem in Geometry. Amer. Math. Monthly 74:6 (1967), 627–640.Google Scholar
- Nelsen, R. B. Heron’s Formula via Proofs Without Words. College Math. J. 32:4 (2001), 290–292.Google Scholar
- Sarnak, P. Integral Apollonian Packings. Amer. Math. Monthly 118:4 (2011), 291–306.Google Scholar