Algebra as geometry

I love this simple, obvious geometric proof that (x + y)^2 = x^2 + 2xy + y^2. I wish someone has shown this to me when they first taught me algebra; it would have made things a lot clearer to me.

[Image from: http://www.mathaware.org/mam/00/master/essays/B3D/2/binomial.html]

Proof that 1 is the largest integer

Let N be the largest positive integer. Then either N = 1 or N > 1.

If N > 1 then N*N > N, which breaks our definition of N as the largest integer. Therefore N = 1.

Via: Futility Closet