Proves persistence of periodic billiard orbits satisfying a combinatorial criterion along paths of deformed polygons.
One Hundred and Twelve Point Three Degree Theorem
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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.
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2026 1verdicts
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Persistence of periodic billiard orbits under domain deformation
Proves persistence of periodic billiard orbits satisfying a combinatorial criterion along paths of deformed polygons.