Summer Fun

I spent a summer in Montanna, not too long ago, but long enough for me to have gotten two degrees in the meantime. My friends and I were working on a ranch and the owner gave us this to think about one evening:

Let A = B.

It follows that Asquared = Bsquared

Also Asquared - AB = Asquared - Bsquared.

Rearranged: A x (A-B) = (A+B) x (A-B).

Dividing each side by the common term we get

A = A+B which is rearranged (via substitution from the original statement) A=A+A= 2A

1=2

I thought it was a neat trick, which it is. But there is good list of them here. Have fun.