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I am looking for examples of geometric proofs of theorems in fields other than euclidean geometry. The more surprising the fact that a geometric proof is possible, the better. As two examples: -From Topics in the Theory of Numbers by Erdos, the proof that square root c is irrational if c is not a perfect square -Isaac Barrow's proof of the Fundamental Theorem of Calculus

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  • $\begingroup$ Also, I know this should probably be community wiki, but don't know how to make it one $\endgroup$ – Gotthold Apr 22 '17 at 12:27
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Here are images for a search for "proofs without words"

https://www.google.com/search?q=proofs+without+words&source=lnms&tbm=isch&sa=X&ved=0ahUKEwj6_tfxirjTAhVE5CYKHZpqCWUQ_AUICSgC&biw=960&bih=650

(I hope this link only answer is OK for community wiki.)

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There is a geometric (or at least, discrete-geometric) proof of Wilson's theorem, $(p - 1)! \equiv -1 \pmod p$ for a prime $p$.

The proof uses regular polygons and star-shaped polygons. See the blog posting by Alexander Bogomolny.

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  • $\begingroup$ This is very pretty! Thanks $\endgroup$ – Gotthold Apr 22 '17 at 13:31

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