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arxiv: 1808.06667 · v1 · submitted 2018-08-20 · 🧮 math.DS

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One Hundred and Twelve Point Three Degree Theorem

George Tokarsky , Jacob Garber , Boyan Marinov , Kenneth Moore
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classification 🧮 math.DS
keywords obtusetrianglepathperiodiceveryangledegreesacute
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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.

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Cited by 1 Pith paper

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  1. Persistence of periodic billiard orbits under domain deformation

    math.DS 2026-05 unverdicted novelty 4.0

    Periodic billiard orbits in polygons that satisfy a combinatorial criterion persist along continuous paths of domain deformations.