Circle Packings from Tilings of the Plane
Number Theory
2023-02-14 v1
Abstract
We introduce a new class of fractal circle packings in the plane, generalizing the polyhedral packings defined by Kontorovich and Nakamura. The existence and uniqueness of these packings are guaranteed by infinite versions of the Koebe-Andreev-Thurston theorem. We prove structure theorems giving a complete description of the symmetry groups for these packings. And we give several examples to illustrate their number-theoretic and group-theoretic significance.
Keywords
Cite
@article{arxiv.2302.06202,
title = {Circle Packings from Tilings of the Plane},
author = {Philip Rehwinkel and Ian Whitehead and David Yang and Mengyuan Yang},
journal= {arXiv preprint arXiv:2302.06202},
year = {2023}
}
Comments
27 pages, 15 figures