Reuleaux Triangle

The Reuleaux triangle is a curve of constant width formed from the intersection of three circular disks, each centered on one vertex of an equilateral triangle and each passing through the triangle's other two vertices, so that the distance between any two parallel supporting lines touching the shape is the same in every direction. It is the simplest and best known non-circular curve of constant width, a class of shapes first studied systematically by Leonhard Euler in the eighteenth century, though the triangle itself is named after the nineteenth century German engineer Franz Reuleaux, who used it and related shapes to illustrate mechanisms capable of converting rotary motion. Because a Reuleaux triangle can rotate within a square while continuously touching all four sides, it forms the basis of drill bits that cut a hole approximately square in cross section, and a shape derived from it approximates the rotor profile used in the Wankel rotary engine.