TITLE: What is the explanation for this visual proof of the sum of squares?
QUESTION [53 upvotes]: Supposedly the following proves the sum of the first-$n$-squares formula given the sum of the first $n$ numbers formula, but I don't understand it.

REPLY [3 votes]: I don't need any votes for my answer, but for a different way to look at it, you can check http://www.maa.org/sites/default/files/Siu15722.pdf