This thread is intended just for fun. My favorite proof of the pythagorean theorem uses algebra, together with a very simple picture. A square is inscribed in another square, and then we use the fact that the whole area is equal to the sum of its parts. The resulting figure consists of an inner square surrounded by four right triangles of equal area. The reason I like this proof more than any other, is because of its utter simplicity. The only thing in algebra you need, is how to carry out the following product: [tex] (a+b)(a+b) [/tex] Using the axioms of algebra, you can conlude that [tex] (a+b)(a+b) = a^2 + 2ab + b^2 [/tex] If anyone is interested in the picture I am referring to, I can provide a link to a site which already has the picture.