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© 1999-2010 by Francis Edward Su

From the Fun Fact files, here is a Fun Fact at the Medium level:

# Reuleaux Wheel

 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 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!

Su, Francis E., et al. "Reuleaux Wheel." Math Fun Facts. <http://www.math.hmc.edu/funfacts>.

Subjects:    geometry, calculus, analysis
Level:    Medium
Fun Fact suggested by:   Michael Moody
Suggestions? Use this form.
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