Spinors and Descartes configurations of disks

2019/09/16 by Jerzy Kocik, Kocik, Jerzy · 3 citations
Mathematics · #Mathematics and Applications #Geometric and Algebraic Topology #Algebraic and Geometric Analysis

paper · pdf · doi:10.48550/arxiv.1909.06994

Abstract

We define spinors for pairs of tangent disks in the Euclidean plane and prove a number of theorems, one of which may be interpreted as a "square root of Descartes Theorem". In any Apollonian disk packing, spinors form a network. In the Apollonian Window, a special case of Apollonian disk packing, all spinors are integral.

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