Math Fun Facts!
hosted by the Harvey Mudd College Math Department created, authored and ©1999-2010 by Francis Su
Subscribe to our RSS feed   or follow us on Twitter.
Get a random Fun Fact!
or
No subject limitations
Search only in selected subjects
    Algebra
    Calculus or Analysis
    Combinatorics
    Geometry
    Number Theory
    Probability
    Topology
    Other subjects
  Select Difficulty  
Enter keywords 

  The Math Fun Facts App!
 
  List All : List Recent : List Popular
  About Math Fun Facts / How to Use
  Contributors / Fun Facts Home
© 1999-2010 by Francis Edward Su
All rights reserved.

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

Reuleaux Wheel

Figure 1
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!

How to Cite this Page:
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.
3.83
 
current
rating
Click to rate this Fun Fact...
    *   Awesome! I totally dig it!
    *   Fun enough to tell a friend!
    *   Mildly interesting
    *   Not really noteworthy
and see the most popular Facts!
New: get the MathFeed iPhone App!

Brings you news and views on math:
showcasing its power, beauty, and humanity

Want another Math Fun Fact?

For more fun, tour the Mathematics Department at Harvey Mudd College!