# pythagorean theorem proof **URL:** \ **Category:** Factual Questions\ **Created:** [March 9, 2001, 10:18pm UTC](https://boards.straightdope.com/t/pythagorean-theorem-proof/57381 "2001-03-09T22:18:53Z")\ **Posts on this page:** 3\ **Page:** 2
**Author:** ![Pies\_R\_Squared](https://avatars.discourse-cdn.com/v4/letter/p/d78d45/32.png) [@Pies\_R\_Squared](https://boards.straightdope.com/u/Pies_R_Squared)\ **Post date:** [March 13, 2001, 3:40am UTC](https://boards.straightdope.com/t/pythagorean-theorem-proof/57381/21 "2001-03-13T03:40:59Z")
**imonacomputer** , One of the ways an author captures my attention is by providing several proofs of the same theorem. Thanks to all those that do. Unfortunately, I think publishers eschew this as unnecessary or wasteful; one of the problems of balancing business with scholarship, I suppose. However, published by the _Mathematical Association of America_, there are the wonderful books _Proofs Without Words_ and _Proofs Without Words II_, both by Roger Nelson. Each contain … _just checking_ … six proofs (without words) of the Pythagorean theorem. Both are currently available and worth the time to look through, especially if you like geometry. As for the ‘8 year-old’ question, I’m at a loss. IMHO, I’m inclined to believe **zut** is on the right track. If the Pythagorean theorem (PT) was proven recently, it was probably in response to the statement of the theorem. There’s a world of difference between proving the PT and discovering the PT, and the former, I’m fairly certain, would be within the capabilities of many prodigious eight-year-olds. Sincerely, Pies ‘R’ Squared ---
**Author:** ![Cabbage](https://avatars.discourse-cdn.com/v4/letter/c/f07891/32.png) [@Cabbage](https://boards.straightdope.com/u/Cabbage)\ **Post date:** [March 14, 2001, 3:51am UTC](https://boards.straightdope.com/t/pythagorean-theorem-proof/57381/22 "2001-03-14T03:51:37Z")
When I first read it, I had no idea what the OP was referring to. Today, however, I ran across the following, which I believe is quite possibly what the OP was referring to (it was on the front page of my local paper this morning, a _Cox News Service_ article, so I’m surprised no one else has mentioned this today). According to the article, in May of 1999 an Atlanta high school student, Josh Klehr, discovered a new geometrical result. He showed it to his teacher, Steve Sigur, and it was recently published in the _American Mathematical Monthly_ and given the name the Klehr-Bliss Theorem (Bliss is another Atlanta area student who did some follow up work). The description of the result in the paper is rather poor, but I believe I can figure out what it’s trying to say (I haven’t checked this work myself, so I can’t say positively I interpret it correctly). OK, so a triangle has various points, or “centers”, associated with it. For example, all the altitudes of a triangle intersect in a certain point; all the bisectors of the angles of a triangle intersect in a certain point; the perpendicular bisectors of the sides intersect in a certain point; and so forth. Klehr discovered a new such point. For background: Given a line with slope m, any line perpendicular to the given line has slope -1/m (negative reciprocal of the original slope). Klehr played around with lines with reciprocal slope (_not_ negative). I’ll call these “reciprocal” lines. So, for a simple example, a reciprocal line to a line with slope 3/7 would have slope 7/3, of course. So start with a triangle, and construct reciprocal lines to each of the three sides of the triangle (it’s not clear from the article _where_ the lines should be constructed, but I tend to assume they mean “reciprocal bisectors” of the sides). These reciprocal lines will intersect in a single point, the new point Klehr found. ---
**Author:** ![imonacomputer](https://avatars.discourse-cdn.com/v4/letter/i/b9bd4f/32.png) [@imonacomputer](https://boards.straightdope.com/u/imonacomputer)\ **Post date:** [March 14, 2001, 4:12pm UTC](https://boards.straightdope.com/t/pythagorean-theorem-proof/57381/23 "2001-03-14T16:12:40Z")
do you or anyone else know a web-site that has more than just the 34 proofs of the pythagorean theorem, because if u do it would help a lot, and i found 1 copy of the book that everyone is saying has 300+ proofs and it was made in 1927, but i haven’t gotten to look at it yet so i hope it’s the right one, thanx [Previous page](https://boards.straightdope.com/t/pythagorean-theorem-proof/57381.md?page=1)