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!
Have students think about why this figure is constant
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.