From:           alexl@daemon.cna.tek.com (Alexander Lopez)
Newsgroups:     sci.math
Subject:        Pythagorean theorem - proofs on the WWW?
Date:           19 Apr 1996 15:40:51 -0700
Organization:   Tektronix, Inc., Redmond, OR
Reply-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 -0700
Newsgroups:     sci.math
Subject:        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 -0400
From:           Godfried Toussaint <godfried@cs.mcgill.ca>
To:             eppstein@ics.uci.edu
Subject:        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