TED-Ed: Why are manhole covers round? - Marc Chamberland

The video explores the concept of curves of constant width, starting with circles and extending to shapes like the Reuleaux triangle. It explains how these shapes maintain a constant distance between parallel lines, making them useful in engineering applications such as drill bits and manhole covers. The video also covers related theorems, including Barbier's theorem, and extends the concept to three-dimensional surfaces like the Reuleaux tetrahedron.

What does Barbier's theorem state about the perimeter of curves of constant width?

How do surfaces of constant width maintain a constant distance between two parallel planes?