### Constant width curves

Curves of constant width satisfy several properties of the circumference and share some of its protagonism. For example, all curves of constant width \(L\) are convex and have the same perimeter [3] (the one of the circumference of diameter \(L\), this is, \(\pi L\)). For any direction, each of the two supporting lines intersects the curve at a single point, and the segment joining these two points is perpendicular to the supporting lines [5]. In addition, we know that among all curves of constant width \(L\) - which therefore have the same perimeter -, the one that encompasses the largest possible area is the circumference [4]; the one that delimits smaller area is the Reuleaux triangle [1].

In the exhibition Matemática Viva there is a cart with exotic wheels whose edges are several curves of constant width (all of them with the same width). The user, who is on a board, when turning the crank, slides without oscillations on a flat road.