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Yeah, this is a nice proof. But somehow it makes me feel like cheating, because it is only simple if you use a level of symbolic algebra that didn't exist in the old Greek days.
A slight variant on it, which is much nicer in my opinion, can be found here: proof #9 on
http://www.cut-the-knot.org/pythagoras/index.shtml
by GreatZamfir on Tue Nov 13th, 2007 at 08:01:19 AM EST
[ Parent ]
It did exist in the old greek days because they stated Pythagoras' theorem in terms of areas of squares built on sides, and addition of areas was a common technique.

At no point in the proof there is a nonhomogenoeous polynomial adding a length to an area, for instance. So Ceebs' argument can be written out in words involving areas.

I think that diagrammatic proof of Pythagoras' theorem may have originated in India?

We have met the enemy, and he is us — Pogo

by Migeru (migeru at eurotrib dot com) on Tue Nov 13th, 2007 at 08:10:50 AM EST
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