* The circle is not the only curve of constant width – so is Reuleaux triangle.

* Any regular odd-sided polygon can be used to construct a curve of constant width.

* For curves of constant width d:

- The perimeter is πd.
- Reuleaux triangles’ area is the smallest, the circle’s area is the greatest.

* A prototype for the Wankel engine was developed. It replaced pistons with a rotor shaped like a Reuleaux triangle.

* A Reuleaux tetrahedron can be modified to form surfaces of constant width (Meissner tetrahedra).

* A general solution for drilling regular even-sided polygons is yet to be found.

* Open question: Meissner tetrahedra have the minimal volume of all 3D surfaces of constant width.

To the MNS presentation