# Graphical Pythagoras

July 3, 2010 at 9:47 PM by Dr. Drang

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

$$4\xb7\left(\frac{ba}{2}\right)+(b-a{)}^{2}={c}^{2}$$Expanding the binomial gives us

$$2ba+({b}^{2}-2ba+{a}^{2})={c}^{2}$$The $ba$ terms cancel, and we’re left with

$${a}^{2}+{b}^{2}={c}^{2}$$as expected. It’s not as cute as the animation, but I like how the algebra works.