*Futility Closet* describes a result that is startling, amazing, and mysterious.

“This is pretty: If you choose *n* > 1 equally spaced points on a unit circle and connect one of them to each of the others, the product of the lengths of these chords equals *n*.”

The *Futility Closet* posting includes an interactive display using Wolfram Technology by Jay Warendorff that let’s you select different *n* and see the results. It also includes a reference to a paper that proves the result; only the paper uses residue theory from complex variables, which seems a bit over-kill, though slick, for such a problem. I found a simpler route.