From:alexl@daemon.cna.tek.com (Alexander Lopez)Newsgroups:sci.mathSubject:Pythagorean theorem - proofs on the WWW?Date:19 Apr 1996 15:40:51 -0700Organization:Tektronix, Inc., Redmond, ORReply-To:alexl@daemon.cna.tek.com

The theorem of Pythagoras is said to have many proofs. I've found four on the WWW (used with the Geometers SketchPad). Are there any sites with more, or sites with historical background on the proofs? -- Alexander Lopez Software Engineering alexl@daemon.CNA.TEK.COM

From:eppstein@ics.uci.edu (David Eppstein)Date:19 Apr 1996 22:26:48 -0700Newsgroups:sci.mathSubject:Re: Pythagorean theorem - proofs on the WWW?

alexl@daemon.cna.tek.com (Alexander Lopez) writes: > The theorem of Pythagoras is said to have many proofs. > I've found four on the WWW (used with the Geometers SketchPad). Are > there any sites with more, or sites with historical background on the > proofs? There is of course a proof in Euclid's Elements, which can be found online in a few places: here is the entry I have from my Geometry Junkyard (http://www.ics.ici.edu/~eppstein/junkyard/), reformatted somewhat from the original HTML: Euclid's Elements (http://www.columbia.edu/~rc142/Euclid.html). Online, in interesting colors, without all those annoying proofs. Also see D. Joyce's Java-animated version (http://aleph0.clarku.edu/~djoyce/java/elements/elements.html), and a manuscript excerpt from a copy in the Bodleian library made in the year 888 (http://www.lib.virginia.edu/science/parshall/elementsamp.html). Of those, Joyce's is the only one likely to have the proof you're looking for. He also has pointers to more online copies of Euclid. It wouldn't hurt to try reading a few actual books, too, as well as just looking online -- contrary to appearances there's a lot of knowledge out there that hasn't been put on the web yet. Most of my geometry books are in my office, but I just took a look at The Penguin Dictionary of Curious and Interesting Geometry, by David Wells, which has the exact citation to Euclid (book I, prop. 47), gives a Chinese proof from before 200BC, and says "far more proofs have been offered of Euclid's theorem than of any other proposition in mathematics" (maybe true but it's hardly the only statement with many proofs; see e.g. my page on Euler's formula, http://www.ics.uci.edu/~eppstein/junkyard/euler/). Wells does list several other proofs and gives citations for more including a 1940 book with 367 of them! Some more historical background on the Pythagorean theorem can be found in Dirk Struik's Consise History of Mathematics, which includes for instance a statement that there is no evidence of ancient Egyptian knowledge of the theorem (contra folklore that they used 3-4-5 triangles to measure right angles). Struik does say though that the theorem was known to the Babylonians and ancient Chinese, although "the first general proof may have been obtained in the Pythagorean school". -- David Eppstein UC Irvine Dept. of Information & Computer Science eppstein@ics.uci.edu http://www.ics.uci.edu/~eppstein/

Date:Sat, 13 Sep 1997 00:13:39 -0400From:Godfried Toussaint <godfried@cs.mcgill.ca>To:eppstein@ics.uci.eduSubject:Pythagoream proofs

Hi David, I found this on your plane geometry page. alexl@daemon.cna.tek.com (Alexander writes: > The theorem of Pythagoras is said to have many proofs. > I've found four on the WWW (used with the Geometers SketchPad). Are > there any sites with more, or sites with historical background on the > proofs? You might like to add to it that there is a site with 23 proofs of the Pythagorean theorem! The URL is: http://www.cut-the-knot.com/pythagoras/index.html Cheers, Godfried