I had never thought of it before, but when you think of it, as you said, the diamond is a square on its side. Therefore, the diagonal has the same number of (whatevers) as the length and/or width. Considering this, it makes sense that a square on its side, with however many whatevers across, is going to be that number, squared. Very interesting observation though, especially the way that you came across it. I have definitely never looked at it from that *angle* before.