TITLE: What are some nice proofs-by-cutting-and-pasting?
QUESTION [6 upvotes]: I enjoy geometric proofs made by cutting-and-pasting. There are some famous examples for Pythagoras's Theorem. Here's another example for the Law of Cosines.

Do you know some other nice proofs using this method?
(NOT for Pythagoras's Theorem, that's been done to death.)
I will add a bounty if someone shows me something particularly insightful.

REPLY [3 votes]: Here's my trigonograph for the Law of Cosines, which involves cutting-and-looking: