Pythagorean theorem four elementary lemmata: Next, each top square is related to a triangle congruent with another triangle related in turn to one of two rectangles making up the lower square. The proof is as follows: This proof, which appears in Euclid's "Elements" as that of Proposition 47 in Book 1, demonstrates that the area of the square on the hypotenuse is the sum of the areas of the other two squares. This is quite distinct from the proof by similarity of triangles, which is conjectured to be the proof that Pythagoras used. We have already discussed the Pythagorean proof, which was
Utah teapot several books and computer graphic journals. The Utah teapot sometimes appears in the "Pipes" screensaver shipped with Microsoft Windows, but only in versions prior to Windows XP, and has been included in the "polyhedra" XScreenSaver hack since 2008. Jim Blinn (in one of his "Project MATHEMATICS!" videos) proves an amusing (but trivial) version of the Pythagorean theorem: Construct a (2D) teapot on each side of a right triangle and the area of the teapot on the hypotenuse is equal to the sum of the areas of the teapots on the other two sides. Loren Carpenter's 1980 CGI film "Vol Libre"