Four bugs chase each other around a square, forever turning but never escaping
Four bugs sit at the corners of a square. At the same instant, each starts crawling at the same constant speed directly toward the bug clockwise from it. As every bug moves, the one it's chasing moves too, so each path curves inward into a spiral. Do the bugs ever actually meet, and if so, how far does each one travel before they do?
Reveal the answer
All four spiral into the exact center and meet there, each having traveled a finite distance exactly equal to the original side length of the square, despite curving the entire way. The problem was first analyzed rigorously by French mathematician Pierre Bouguer in 1732, and the spiraling paths it produces are called pursuit curves, later popularized by Martin Gardner as the "four bugs" problem.