# Graphical Pythagoras

You may have seen this clever animated GIF floating around the intertubes lately. The original seems to live at http://i.imgur.com/DrROq.gif, but I have no idea who created it.

To me, the whole thing could have been done with just this frame.

Each of the four pink triangles has an area of $ba/2$, the little blue square in the center has an area of $(b-a)^2$, and the big square formed by the hypotenuses has an area of $c^2$. So

Expanding the binomial gives us

The $ba$ terms cancel, and we’re left with

as expected. It’s not as cute as the animation, but I like how the algebra works.