Hans Havermann> Dan Asimov: Does anyone know who first thought of the following proof that sqrt(2) is irrational? It looks like Tom M. Apostol's proof, published as "Irrationality of The Square Root of Two - A Geometric Proof" in the American Mathematical Monthly, November 2000, pp. 841–842. Years ago, Conway said, perhaps on this list, that he was working on a book of Extreme Proofs. His version of this one was to cut (or fold) a square of paper along the diagonal, making an isosceles right triangle. Label the sides a,a,b. Then bisect-fold one of the 45˚ angles. This creates an obvious right-angled b-a,b-a,2a-b. --rwg