TITLE: Beautiful, simple proofs worthy of writing on this beautiful glass door
QUESTION [19 upvotes]: What are some of the more beautiful proofs you know? I am measuring beauty in two dimensions -- first, how conceptually elegant is it and second, how aesthetically pleasing is it. 
Context: 
I work at a econ consulting firm. We're mostly math majors or very quantitative econ majors. A buddy and I are trying to decide what to write on the glass door to the office we share. Currently it has a graph of quality of Brad Pitt's movies against how frequently he was shirtless in that movie. Time to upgrade that...

REPLY [6 votes]: Here are a few visual proofs that 
$$\text{arctan}(1) + \text{arctan}(2) + \text{arctan}(3) = \pi$$
One by user KennyTM:


More by user dldarek:


I think the lattice nature of the proofs would look nice on a door.