# 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 \cdot \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.