The game of billiards is played on a rectangular table (known as a billiard table) upon which balls are placed. One ball (the "cue ball") is then struck with the end of a "cue" stick, causing it to bounce into other balls and reflect off the sides of the table. Real billiards can involve spinning the ball so that it does not travel in a straight line, but the mathematical study of billiards generally consists of reflections in which the reflection and incidence angles are the same. However, strange table shapes such as circles and ellipses are often considered. The popular 1959 animated short film Donald in Mathmagic Land features a tutorial by Donald Duck on how to win at billiards using the diamonds normally inscribed around the edge of a real billiard table.
Many interesting problems can arise in the detailed study of billiards trajectories. For example, any smooth plane convex set has at least two