2012 will be, in several countries, a presidential election year. Some decades ago, candidates were not always supposed to spend months on some
demagogicdemocratic debates, but had time to spend on more important problems. Like mathematics… For instance, a congressman, who became the 20th president of the United States, James Garfield, gave the following proof to the Pythagorean theorem (actually, he wrote that proof five years before he become President). The legend claims that he found this proof in 1876 during a mathematics discussion with some of the members of Congress… Those were good old days, when politicians were interested in mathematics, and sciences. The proof he suggested was the following
i.e. , since
I found that nice graph in Roger Nelsen’s book. For more details, Klebe (1995), or on wikipedia. And for those who love proofs without words, look at the 96 geometrical proofs of the Pythagorean theorem mentioned on http://www.cut-the-knot.org/.