Bodies of Constant Width in Art, Design, and Engineering

Abstract

As we mentioned before, a normal wheel (rotating around a fixed axis) must be circular in shape to allow smooth forward motion without vertical bumps. However, a cylindrical roller does not require a circular cross section to allow smooth forward motion. In fact, any curve of constant width, such as the Reuleaux triangle, may be used as a cylindrical roller. Besides this nice property, the curves of constant width, in particular, the Reuleaux triangle, have been exploited by engineers, artists, and designers to obtain wonderful objects and number of ingenious mechanisms.