Reuleaux Triangle in Architecture and Applications

Abstract

The Reuleaux triangle is a figure with the remarkable property of having constant width, a typical property of the circle. It takes its name from Franz Reuleaux, a 19th century German engineer, who studied its properties, in particular the ones related to applications to mechanics. However, this figure was previously known: actually, we find it in the shape of the windows and in the ornaments of some Gothic architecture. Furthermore, Leonardo da Vinci, to represent the terrestrial globe, used eight Reuleaux triangles, each one corresponding to an octant of the spherical surface. Even the mathematician Euler encountered this figure in his study of geometric forms with constant width.