Optimal Packings of Two to Four Equal Circles on Any Flat Torus
Metric Geometry
2019-05-15 v2
Abstract
We find explicit formulas for the radii and locations of the circles in all the optimally dense packings of two, three or four equal circles on any flat torus, defined to be the quotient of the Euclidean plane by the lattice generated by two independent vectors. We prove the optimality of the arrangements using techniques from rigidity theory and topological graph theory.
Keywords
Cite
@article{arxiv.1708.05395,
title = {Optimal Packings of Two to Four Equal Circles on Any Flat Torus},
author = {Madeline Brandt and William Dickinson and AnnaVictoria Ellsworth and Jennifer Kenkel and Hanson Smith},
journal= {arXiv preprint arXiv:1708.05395},
year = {2019}
}
Comments
27 pages, 14 figures