Pythagoras

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Pythagoras

Robert P Crease explains why Pythagoras's theorem is not simply a way of computing hypotenuses, but an emblem of the discovery process itself

Pythagoras's theorem changed the life of the British philosopher Thomas Hobbes (1588- 1679). Until he was 40, Hobbes was a talented scholar exhibiting modest originality. Versed in the humanities, he was dissatisfied with his erudition, and had little exposure to the exciting new breakthroughs achieved by Galileo, Kepler and other scientists who were then revolutionizing the scholarly world.

One day, in a library, Hobbes saw a display copy of Euclid's Elements opened to Book I Proposition 47, Pythagoras's theorem. He was so astounded by what he read that he used a profanity that his first biographer, John Aubrey, refused to spell out: " 'By G__' Hobbes swore, 'this is impossible!'." He read on, intrigued. The demonstration referred him to other propositions, and he was soon convinced that the startling theorem was true.

http://physicsweb.org/articles/world/19/1/3/1

[information_synthesis]

The Pythagorean Theorem- The Crown Jewel of Mathematics:
http://www.scribd.com/doc/2559569/The-Pythagorean-Theorem-Crown-Jewel-of-Mathematics

The Pythagorean Proposition (370 Proofs of the Pythagorean Theorem):
http://www.eric.ed.gov/ERICDocs/data/ericdocs2sql/content_storage_01/0000019b/80/32/54/86.pdf

Quotation from opening page:

The text includes a biography of Pythagoras and an account of historical data pertaining to his proposition. The remainder of the book shows 370 different proofs, whose origins range from 900 B.C. to 1940 A.D. They are grouped into the four categories of possible proofs: Algebraic (109 proofs); Geometric (255 proofs); Quaternionic (4 proofs); and those based on mass and velocity, Dynamic (2 proofs). Also included are five Pythagorean magic squares; the formulas of Pythagoras, Plato, Euclid, Maseres, Dickson, and Martin for producing Pythagorean triples; and a bibliography with 123 entries.

For another collection of Pythagorean Theorem proofs you can find some online here:
http://www.cut-the-knot.org/pythagoras/index.shtml
http://www.cut-the-knot.org/pythagoras/FalseProofs.shtml