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My favorite theorem is the Pythagorean Theorem. It is much better than EVAN'S FAVORITE THEOREM_MA375Fall2008walther.

(No seriously, I chose it before looking at his page) --

Here it is $ a^2+b^2=c^2 $

It's one of those theorems that is surprising at first. When I saw the proof of it I was pretty amazed. There's an image of it here.

If I couldn't choose that one, I would probably choose the four color theorem, since it's pretty easy to understand.

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Basic linear algebra uncovers and clarifies very important geometry and algebra.

Dr. Paul Garrett