Computation and Billiards in Triangles
Surprisingly, there are many open problems about billiards in triangles.
The most notable question is "Does every triangle have a periodic billiard
path?" This question has been resolved in the acute and right triangle
cases, and also when a triangle has rational angles. The resolution of the
rational case involves Teichmuller theory of compact surfaces, but this
resolution gives rise to further open questions (e.g. "Classify the Veech
triangles.")
Recently, Rich Schwartz and I have approached triangular billiards from a
computational direction, yielding new results. I will demonstrate our
program, McBilliards, and discuss some of these new results. I will also
discuss some of the computational problems faced in constructing such a
program.