* 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