Around the wheel

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.

To know more...