One Hundred and Twelve Point Three Degree Theorem
Dynamical Systems
2018-08-22 v1
Abstract
It has been known since Fagnano in 1775 that an acute triangle always has a periodic billiard path, namely the orthic triangle. It is currently unknown whether every obtuse triangle has a periodic path. In 2006, Schwartz showed that every obtuse triangle with obtuse angle at most 100 degrees has a periodic path. The aim of this paper is to show that every obtuse triangle with obtuse angle at most 112.3 degrees has a periodic path using a computer assisted proof.
Keywords
Cite
@article{arxiv.1808.06667,
title = {One Hundred and Twelve Point Three Degree Theorem},
author = {George Tokarsky and Jacob Garber and Boyan Marinov and Kenneth Moore},
journal= {arXiv preprint arXiv:1808.06667},
year = {2018}
}