Pat Hooper's Abstract

We mark the edges of our triangles by 1,2, and 3. The symbolic dynamics of a periodic billiard path in a marked triangle is the periodic sequence in {1,2,3}, corresponding to the sequence of edges hit by the billiard ball. Given a periodic sequence {a_n} in {1,2,3}, consider the set T({a_n}) of all marked triangles which realize this sequence by a periodic billiard path.

I will discuss the proof of the fact: "If T({a_n}) contains an open set, then it contains only acute or only obtuse triangles." In particular, if T({a_n}) is open, then it contains no right triangles. Suprisingly, the proof is essentially topological.