What is the most elegant proof of the Pythagorean theorem? [closed]

The Pythagorean Theorem is one of the most popular to prove by mathematicians, and there are many proofs available (including one from James Garfield).

What’s the most elegant proof?

My favorite is this graphical one:

alt text

According to cut-the-knot:

Loomis (pp. 49-50) mentions that the
proof “was devised by Maurice Laisnez,
a high school boy, in the
Junior-Senior High School of South
Bend, Ind., and sent to me, May 16,
1939, by his class teacher, Wilson
Thornton.”

The proof has been published by Rufus
Isaac in Mathematics Magazine, Vol. 48
(1975), p. 198.

Answer

I really like this one (image taken from cut-the-knot #4)

alt text

along with

(a+b)2=412ab+c2
c2=a2+b2

It’s so clear and easy …

Note: Just to make it clear, the side of the square is a+b

Attribution
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