Problem Solving in Geometry—A Sequence of Reuleaux Triangles

Abstract

A Reuleaux (pronounced “rue-low”) triangle is an example of a curve of constant width. The distance between parallel tangents is the same no matter which direction is used. A Reuleaux triangle ABC can be constructed (see fig. 1) by starting with an equilateral triangle ABC with sides of length w and drawing arcs of circles connecting two vertices, with the third vertex as center. Figure 1 also shows two pairs of parallel tangents. The length of the side of the equilateral triangle is the constant width for the associated Reuleaux triangle.