Pythagorean theorem animation

    Caption: An animation giving a visual proof of the Pythagorean theorem.

    Proof explicated:

    1. The overall square never changes size.
    2. The grey area never changes size. Grey triangles just get rotated.
    3. Therefore the black area never changes size.
    4. c is the hypotenuse of a grey triangles.
    5. a and b are, respectively, the opposite and adjacent (or vice versa) of a grey triangles.
    6. The black area is c**2 in one configuration.
    7. The black area is a**2+b**2 in another configuration.
    8. Therefore c**2=a**2+b**2 which is the Pythagorean theorem.
    9. Q.E.D.

    The visual proof is NOT complete. One actually has to assume that one has a 2-dimensional Euclidean space with the properties of such a space. For further explication, see, e.g., Roger Penrose, The Road to Reality, 2004, p. 25--33).

    Credit/Permission: © John Blackburne (AKA User:JohnBlackburne), 2010 / Creative Commons CC BY-SA 3.0.
    Image link: Wikipedia: File:Pythag anim.gif.
    Local file: local link: babylonian_pythagoras_proof.html.
    File: Babylonian astronomy file: babylonian_pythagoras_proof.html.