Robyn Miller

We provide a complete characterization of billiard trajectory hitting sequences () () on [pi] -isosceles triangles for n [GREATER-THAN OR EQUAL TO] 2. The case of the [pi] -isosceles triangle is pren 4 sented in detail. When n equals two or three, these triangles tile the plane. For n greater than or equal to four, this is no longer the case. On the two isosceles tri() angles that tile the plane, as well as the [pi] -isosceles triangle, we provide combi4 natorial renormalization schemes that apply directly to hitting sequences given in a three letter aphabet of triangle side labels. Although cutting sequences have been characterized on related translation surfaces, this is the first analysis of billiard trajectory hitting sequences in triangles.