Curve of constant width

Summary

A curve of constant width is the boundary of a plane convex body with this property. Every two parallel supporting lines of the body are at the same distance, called the width. The circle is the simplest example, but there are many others, such as the Reuleaux triangle. Curves of constant width are a classical source of extremal problems in plane convex geometry. All of them with a given width have the same length, but their areas differ.