Trisect any triangle's angles and find a perfect equilateral triangle hiding inside
Take any triangle at all — scalene, obtuse, as lopsided as you like — and trisect each of its three angles into three equal parts. Look at where the trisector lines nearest each side cross each other. What shape do the three intersection points form?
Reveal the answer
They always form a perfect equilateral triangle, no matter what the original triangle looked like. Mathematician Frank Morley discovered this in 1899, but it seemed so surprising that it circulated only informally among mathematicians for about 15 years before anyone bothered to publish a proof. It's now known as Morley's trisector theorem and remains one of the most unexpected results in elementary geometry.