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.
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"from the vertices" -> "form the vertices"
Also, you might want to close comments on the human/chimp split post, which is bubbling over with spam (both comment and TrackBack).
I remember this from High School. Don't have the name for it, and I no longer have the brain muscle to come up with a proof.
Start with any quadrilateral. Bisect the sides. Call the points of bisection A, B, C, D. The lines AC and BD intersect at right angles.
nod and tip of the hat.
'ppreciate the mention.