Ever since I was in grade school I have been fascinated with the idea that the Pythagorean theorem, or any other universally respected theorem, could be wrong. When I was younger I found a little proof I made to disprove it, and I came across it in an old notebook of mine. Now after taking calculus and other more advanced maths I see that Pythagoras could not be wrong, however, I am having trouble actually disproving the proof I made to disprove Pythagoras's theorem, if that makes sense. I may just be having a serious brain fart so don't kill me. The proof I made was this: Make 4 congruent right triangles with side lengths of "a" and "b" and a hypotenuse with a length "c" and put the triangles together to make a square where the hypotenuses of the triangles are on the outside of the square. it should look like this: http://4.bp.blogspot.com/-YF-2E8vTRLs/TmoSmBD65wI/AAAAAAAABX8/BPFkCMM0vGE/s1600/QST.png Obviously the area of the triangle is A=c^2, the Area could also be the area of each triangle A=1/2ab, there are 4 of them so it becomes A=2ab. Through substitution we get c^2=2ab. c^2=2ab doesn't agree with the Pythagorean theorem, the problem I have having is explaining why this is so... I cant find an error in my logic. So can you guys help me out and tell me where I went wrong?