I was really impressed by this post from Polymathematics. He discusses a proof of Morley’s Theorem, which is a result from Euclidean geometry. Start with any triangle. Trisect each of the three angles. Then the points of intersection of pairs of adjacent trisectors from the vertices of an equilateral triangle. Take one look at the pictures Polymathematics provides and you’ll see what I mean. The details of the proof are ingenious, and not too hard to follow. Highly recommended.