A *Reuleaux Triangle* is a plump triangle with rounded edges, formed in the following way: take the three points at the corners of an equilateral triangle, and connect each pair of points by a circular arc centered at the remaining point.

This triangle has some amazing properties. It is *constant-width*, meaning that it will hug parallel lines as it rolls. By rotating the centroid of the Reuleaux triangle appropriately, the figure can be made to trace out a square, perfect except for slightly rounded corners!

This idea has formed the basis of a drill that will carve out squares!

And, what do you think the ratio of its circumference to its width is?

Amazing fact: it is PI!

**Presentation Suggestions:**

Have students think about why this figure is constant width.

**The Math Behind the Fact:**

There are many other convex, constant-width figures, such as the circle and various Reuleaux polygons, and they all satisfy the same ratio of circumference to width!

**How to Cite this Page:**

Su, Francis E., et al. “Reuleaux Wheel.” *Math Fun Facts*. <https://www.math.hmc.edu/funfacts>.

**Fun Fact suggested by: **

Michael Moody