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>.
