Favourite proofs with a visualization

Question

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.

Answer 1

You'll find many of such "proofs" here. The first one is particularly freaky.

I'm personally a fan of using graphs of functions to show their properties. Edgy, right?

Answer 2

Roger B. Nelsen's books Proofs Without Words: Exercises in Visual Thinking, Vol I and II are very nice. I particularly like this construction of his.

Answer 3

Claudi Alsini and Roger Nelson have published a series of excellent books about what some people call "proofs without words." The most recent of these books is called Icons of Mathematics: An Exploration of Twenty Key Images, was published by MAA in 2011 and has both appealing ideas and mathematics.