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Bike with Square Wheels - mklabgr - 07-27-2026 Bike with Square Wheels Summary The article explores the surprising mathematical fact that square wheels can provide a perfectly smooth ride when they roll over a specially designed road. Instead of a flat surface, the road consists of a sequence of inverted catenaries—the upside-down form of the curve made by a hanging chain—which keeps the wheel’s axle moving at a constant height. The post highlights the famous square-wheeled tricycle at Macalester College, inspired by an earlier exhibit at San Francisco’s Exploratorium and developed by mathematician Stan Wagon.  It explains how this idea led to broader research on the relationship between wheel shapes and road profiles, showing that many non-circular wheels, including pentagons, hexagons, ellipses, cardioids, and other unusual shapes, can also roll smoothly when paired with the correct track. Interestingly, triangular wheels do not work on the same type of surface. The article demonstrates how an apparently impossible concept becomes an elegant application of geometry and calculus, revealing that smooth motion depends not only on the wheel but also on the mathematical design of the road.  ARTICLE