Re: can Pythagoras's theorem be proved without the idea of the area of a rectangle being a*b
- From: "Shmuel (Seymour J.) Metz" <spamtrap@xxxxxxxxxxxxxxxxxxxxxxxxxx>
- Date: Wed, 11 Oct 2006 08:07:17 -0300
In <1160525673.547601.241610@xxxxxxxxxxxxxxxxxxxxxxxxxxx>, on
10/10/2006
at 05:14 PM, "david petry" <david_lawrence_petry@xxxxxxxxx> said:
Use high school geometry, similar triangles, etc.
Just establishing the existence of similar triangles takes some work.
It's very easy to assume the nature of the metric without realizing
it.
In this case, "add a small increment to 'b', keeping 'a' fixed" is ill
defined, and by the time you pin down what you mean by that you may
have slipped more in than you expected.
Draw a picture.
A picture of what? The Devil is in the details. Drawing pictures is
convenient if I want to convince someone that I can square the circle;
it's no substitute for a proof. At best a picture is an aid to
understanding a proof, but even there it tends to obscure the
existence of special cases.
--
Shmuel (Seymour J.) Metz, SysProg and JOAT <http://patriot.net/~shmuel>
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