A Visual Proof

The great mathematician
Robert P. Langlands
is 70 today.

In honor of his expository work–
notably, lectures at
The Institute for Advanced Study
on “The Practice of Mathematics“
and a very acerbic review (pdf) of
a book called Euclid’s Window—
here is a “Behold!” proof of
the Pythagorean theorem:

The image “http://www.log24.com/log/pix06A/Pythagorean_Theorem.jpg” cannot be displayed, because it contains errors.

The picture above is adapted from
 a sketch by Eves of a “dynamical”
proof suitable for animation.

The proof has been
 described by Alexander Bogomolny
as “a variation on” Euclid I.47.
Bogomolny says it is a proof
by “shearing and translation.”

It has, in fact, been animated.
The following version is
by Robert Foote:
The image “http://www.log24.com/log/pix06A/RobertFooteAnimation.gif” cannot be displayed, because it contains errors.