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(a+b)*(a+b)-n2=4(a*b)/2 (from the diagram)

a2+b2+2ab=2ab+n2

so a2+b2=n2

Life should consist in at least fifty percent pure waste of time, and the rest doing what you please.

by ceebs (bunchofwankers (at) gmail (dot) com) on Tue Nov 13th, 2007 at 07:48:34 AM EST
[ Parent ]
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
[ Parent ]

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