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 Easy level:

Napoleon's Theorem

Figure 1
Figure 1

Take any generic triangle, and construct equilateral triangles on each side whose side lengths are the same as the length of each side of the original triangle.

Surprise: the centers of the equilateral triangles form an equilateral triangle!

Presentation Suggestions:
Show the truth of the statement using some extreme cases for the initial triangle (a particularly instructive example is a triangle with one sidelength very close to zero).

The Math Behind the Fact:
This theorem is credited to Napoleon, who was fond of mathematics, though many doubt that he knew enough math to discover it!

How to Cite this Page:
Su, Francis E., et al. "Napoleon's Theorem." Math Fun Facts. <http://www.math.hmc.edu/funfacts>.

Subjects:    geometry
Level:    Easy
Fun Fact suggested by:   Michael Moody
Suggestions? Use this form.
3.81
 
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!
Get the Math Fun Facts
iPhone App!

Want another Math Fun Fact?

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