Roughly, a periodic billiard path is a polygon P is called
stable if any polygon P', which is sufficiently similar to P, has a periodic billiard
path which bounces off the same sequence of edges. We will discuss the
resolution of a conjecture of Vorobets, Galperin, and Stepin.
No right triangle has a stable periodic billiard path. We will also discuss a
slight generalization. Namely, stable perioidic billiards paths in acute and
obtuse triangle can be distinguished by the sequence
of edges they hit.