Proof of Descartes circle formula and its generalization clarified

2019/10/21 by Jerzy Kocik, Kocik, Jerzy · 1 citation
Mathematics · Physics and Astronomy · #15A63 #51N20 #Advanced Mathematical Theories and Applications #Analytic Number Theory Research #FOS: Mathematics #History and Overview (math.HO) #Mathematics and Applications #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.1910.09174

openalex publication_date 2019/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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

Citations

• A theorem on circle configurations

Cited by

• The Hofstadter Butterfly: Bridging Condensed Matter, Topology, and Number Theory

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• Apollonian Circle Packings: Number Theory
• Beyond the Descartes circle theorem
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