Spinors and Descartes configurations of disks

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.

arXiv comment21 pages, 14 figures

References in corpus (1)

• A theorem on circle configurations

Cited by in corpus (3)

• Spinors, lattices, and classification of integral Apollonian disk packings
• Apollonian coronas and a new Zeta function
• Tessellations and Descartes disk configurations