Figure 1

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 constantwidth, 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, constantwidth 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.
<http://www.math.hmc.edu/funfacts>.
