2021
DOI: 10.48550/arxiv.2105.12950
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Integral spinors, Apollonian disk packings, and Descartes groups

Jerzy Kocik

Abstract: We show that every irreducible integral Apollonian packing can be set in the Euclidean space so that all of its tangency spinors and all reduced coordinates and co-curvatures are integral. As a byproduct, we prove that in any integral Descartes configuration, the sum of the curvatures of two adjacent disks can be written as a sum of two squares. Descartes groups are defined, and an interesting occurrence of the Fibonacci sequence is found.

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