Proof of Descartes circle formula and its generalization clarified

Abstract

In his talk "Integral Apollonian disk Packings" Peter Sarnak asked if there is a "proof from the Book" of the Descartes theorem on circles. A candidate for such a proof is presented in this note

3 pages, 1 figure. This is a succinct and clarified version of the proof presented in arXiv:0706.0372

References in corpus (1)

• A theorem on circle configurations

Cited by in corpus (3)

• Spinors, lattices, and classification of integral Apollonian disk packings
• Apollonian depth, spinors, and the super-Dedekind tessellation
• Integral spinors, Apollonian disk packings, and Descartes groups