Build equilateral triangles outward on any triangle's sides, then look at their centers
Take any triangle, however lopsided, and construct an equilateral triangle pointing outward on each of its three sides. Mark the center of each of those three new triangles. What shape do the three centers always form?
Reveal the answer
A perfect equilateral triangle, no matter what shape the original triangle was. The result is traditionally credited to Napoleon Bonaparte, an amateur mathematics enthusiast, though historians doubt he actually discovered it; it remains a favorite because such a rigid, symmetric outcome falls out of an arbitrarily messy starting triangle.