(Originally posted at http://joelnoche.multiply.com/journal/item/19/Billiard-Paths on September 3, 2010 10:08 PM)
Many years ago (perhaps around 1998), I bought a copy of Joseph O’Rourke’s Art Gallery Theorems and Algorithms (published in 1987) from a BOOKSALE outlet. One of my favorite sections was the one on Mirrors (section 10.5) because it had a lot of open problems on illumination and billiard paths. I have written a short article (Periodic Billiard Paths in Triangles) targeted at undergraduates. It’s a summary of one open problem: does every triangle have a periodic billiard path?