Classification of rational angles in plane lattices
Number Theory
2024-04-09 v3 Metric Geometry
Abstract
This paper is concerned with configurations of points in a plane lattice which determine angles that are rational multiples of . We shall study how many such angles may appear in a given lattice and in which positions, allowing the lattice to vary arbitrarily. This classification turns out to be much less simple than could be expected, leading even to parametrizations involving rational points on certain algebraic curves of positive genus.Bulletin of the American Mathematical Society
Cite
@article{arxiv.2005.13598,
title = {Classification of rational angles in plane lattices},
author = {Roberto Dvornicich and Francesco Veneziano and Umberto Zannier},
journal= {arXiv preprint arXiv:2005.13598},
year = {2024}
}
Comments
36 pages, 6 pictures. First part of arXiv:2404.02559