I am very enthusiastic about this proof, which could readily be used in the third or fourth grade. I expect to use it at that level. The proof is both sound and intuitive: kids would be able not only to see that it works but also to have a good sense of why. Two questions:#1: Any history? Is it ten years old or a thousand? At minimum, I'd like to know what I can call the proof (other than "Proof #9 at http://www.cut-the-knot.com/pythagoras";). Have you any leads on the discoverer, or at least the medieval abbey at which it was discovered?
#2: Are you aware of any educational supply company that produces a jigsaw-puzzle version of the proof? With such materials and a little guidance, kids could discover the theorem for themselves. Custom manufacture is of course a possibility, but it would be expensive. If there are copyright considerations, I would like to know about these as well.
Thanks in advance,
Peter Brown
Can't answer your questions off the top of my head. I am pretty sure though that the proof must have been known to the ancients. There could not possibly be any copyright restrictions.In the proof #35 there's a link to a fellow who sells a 5 pieces puzzle that goes with the proof. His product may not be very suitable for 3-4 graders as the pieces have sharp edges. However, it is remarkable that even such a simple puzzle is not altogether trivial to solve. I'd be utterly surprised if anybody discovered the Pythagorean theorem using that puzzle.
Proof #9 may be a different matter. Indeed, all you need is 4 equal right angled triangles. First arrange the triangles as to make a square hole as in the first of the diagrams in the proof and make the students trace the outer square. Then rearrange they triangles as in the second diagram.