How Many Proofs of the Pythagorean Theorem?
Date: 03/27/2003 at 19:11:14 From: Coco Subject: The Pythagorean Theorem I was wondering if you know the exact number of proofs of the Pythagorean Theorem in existence.
Date: 03/27/2003 at 23:20:16 From: Doctor Peterson Subject: Re: The Pythagorean Theorem Hi, Coco. Even if I had every single proof anyone had ever written, I couldn't count them, because I couldn't decide how different two proofs have to be in order to be counted. But someone wrote a book in which he showed 367 proofs that were distinct enough to bother writing about separately. This page lists 41 of them: Pythagorean Theorem and its Many Proofs - Bogomolny http://www.cut-the-knot.org/pythagoras/index.shtml and has a footnote: W.Dunham [Mathematical Universe] cites a book The Pythagorean Proposition by an early 20th century professor Elisha Scott Loomis. The book is a collection of 367 proofs of the Pythagorean Theorem and has been republished by NCTM in 1968. Again, this page Pythagoras' Theorem http://www.sunsite.ubc.ca/DigitalMathArchive/Euclid/java/html/ pythagoras.html describes the book just a little differently: Elisha Loomis, The Pythagorean Proposition, National Council of Teachers of Mathematics, 1968. This eccentric book was first compiled in 1907, first published in 1928 (at a price of $2.00!), and reissued in this edition. It contains 365 more or less distinct proofs of Pythagoras' Theorem. The total effect is perhaps a bit overwhelming, and the quality of the figures is very poor, but nonetheless there are a few gems distributed throughout. The following page The Pythagorean Theorem - Jim Loy http://www.jimloy.com/geometry/pythag.htm says The book The Pythagorean Proposition, By Elisha Scott Loomis, is a fairly amazing book. It contains 256 proofs of the Pythagorean Theorem. It shows that you can devise an infinite number of algebraic proofs, like the first proof above. It shows that you can devise an infinite number of geometric proofs, like Euclid's proof. And it shows that there can be no proof using trigonometry, analytic geometry, or calculus. The book is out of print, by the way. I'm not sure which number is right, but it appears that you can't count the number of distinct proofs, in any case. If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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