In Disney’s 1959 film Donald in Mathmagic Land, Donald Duck, inspired by the narrator’s descriptions of the geometry of billiards, energetically strikes the cue ball, sending it ricocheting around the table before it finally hits the intended balls. Donald asks, “How do you like that for mathematics?”
Because rectangular billiard tables have four walls meeting at right angles, billiard trajectories like Donald’s are predictable and well understood — even if they’re difficult to carry out in practice. However, research mathematicians still cannot answer basic questions about the possible trajectories of billiard balls on tables in the shape of other polygons (shapes with flat sides). Even triangles, the simplest of polygons, still hold mysteries.
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