The Descartes circles theorem and division by zero calculus

2017/11/14 by Hiroshi Okumura, Okumura, Hiroshi, Saburou Saitoh +1 · 1 citation
Mathematics · #01A27 #01A45 #03C99 #51M04 #Algebraic and Geometric Analysis #FOS: Mathematics #History and Overview (math.HO) #Mathematical and Theoretical Analysis #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.1711.04961

openalex publication_date 2017/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

From the viewpoint of the division by zero (0/0=1/0=z/0=0) and the division by zero calculus, we will show that in the very beautiful theorem by Descartes on three touching circles is valid for lines and points for circles except for one case. However, for the exceptional case, we can obtain interesting results from the division by zero calculus.

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