Pythagoras Theorem

There are two names :
for Chinese : Gougu theorem
for western : Pythagorean theorem or Pythagoras' theorem

This theorem may have more known proofs than any other (the law of quadratic reciprocity being also a contender for that distinction); the book Pythagorean Proposition, by Elisha Scott Loomis, contains 367 proofs.
Some arguments based on trigonometric identities (such as Taylor series for sine and cosine) have been proposed as proofs for the theorem. However, since all the fundamental trigonometric identities are proved using the Pythagorean theorem, there cannot be any trigonometric proof. (See also begging the question.)

You may visit the followings for the proofs of pyth. theorem :
Some animated proofs of the Pythagorean theorem at Math Is Fun
Proof of the Pythagorean theorem
Pythagorean theorem with interactive animation
Pythagorean Theorem (more than 70 proofs from cut-the-knot)