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As a fan of 'visual' proofs, I love the book Visual Complex Analysis by Tristan Needham.

For example, this picture http://en.wikipedia.org/wiki/File:Pythagoras_algebraic2.svg leads quickly to Pythagoras's theorem.

I'd like to know which are your favourite examples of a clever visualization that proves or helps the intuition for a proof.

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    I've always been fond of the topological proof that all non-constant polynomials have a root, because, even though the rigors of proving the basic homotopy stuff is extreme, it "makes sense."2012-02-10
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    You can see my answer in [is this theorem true in optimization theory](http://math.stackexchange.com/questions/152722/is-this-theorem-true-in-optimization-theory/152730#152730)2012-06-03

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