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*. <https://www.math.hmc.edu/funfacts>.

**Fun Fact suggested by: **

Michael Moody