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:

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)

along with

(a+b)2=4⋅12ab+c2

⇔c2=a2+b2

It’s so clear and easy …

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

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