Random triangles on flat tori
Combinatorics
2020-03-19 v1 Geometric Topology
Probability
Abstract
Inspired by classical puzzles in geometry that ask about probabilities of geometric phenomena, we give an explicit formula for the probability that a random triangle on a flat torus is homotopically trivial. Our main tool for this computation involves reducing the problem to new invariant of measurable sets in the plane that is unchanged under area-preserving affine transformations. Our result show that this probability is minimized at all rectangular tori and maximized at the regular hexagonal torus.
Keywords
Cite
@article{arxiv.2003.08190,
title = {Random triangles on flat tori},
author = {Olivier Glorieux and Andrew Yarmola},
journal= {arXiv preprint arXiv:2003.08190},
year = {2020}
}