Visualizing mathematics

I love visual proofs of mathematical theorems. One visual proof I use quite often in my design courses (CEP817 or CEP917) is a visual proof of the fact that the sum of consecutive odd numbers is a square number.

In other words:

1 + 3 = 4 = 2²

1 + 3 + 5 = 9 = 3²

1 + 3 + 5 + 7 = 16 = 4²

… and so on.

Mathematically speaking that translates to

Now one can go about proving this fact this through algebra OR one could just do it visually. Check out this image below,

… or better still go to this applet

Pretty cool huh?

Looking for the above applet led me to this other cool visual proof for

Check it out.