Periodic Billiards in Isosceles Triangles

TL;DR

This paper explores the relationship between periodic billiard trajectories in isosceles triangles and right triangles, revealing implications for the existence of stable trajectories and properties of orbit tiles.

Contribution

It establishes a connection between periodic trajectories in isosceles and right triangles, providing new insights into their stability and orbit tile properties.

Findings

Periodic trajectories in isosceles triangles correspond to those in right triangles.

The relationship impacts the existence of stable trajectories.

It influences the structure of orbit tiles.

Abstract

Any periodic trajectory on an isosceles triangle gives rise to a periodic trajectory on a right triangle obtained by identifying the halves of the original triangle. We examine the relationship between periodic trajectories on isosceles triangles and the trajectories on right triangles obtained in this manner, and the consequences of this relationship for the existence of stable trajectories on isosceles triangles and the properties of their orbit tiles.