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From: bs@faron.UUCP (Robert D. Silverman)
Newsgroups: net.puzzle
Subject: Re: A somewhat different geometry problem
Message-ID: <386@faron.UUCP>
Date: Sat, 16-Nov-85 22:11:47 EST
Article-I.D.: faron.386
Posted: Sat Nov 16 22:11:47 1985
Date-Received: Sun, 17-Nov-85 06:37:59 EST
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Organization: The MITRE Coporation, Bedford, MA
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> I was rather impressed with what seems to be the first
> real new "discovery" made by a computer program.  Seems
> a program for producing proofs of theoerms in elementary
> geometry came up with a truly elegant proof that the
> sides of an isoceles triangle are equal.  Of course,
> this is proved in elementary geometry courses, normally
> by drawing an auxiliary line (altitude), etc.  But the
> program, which "knew" about congruent triangles, came
> up with a beautiful short proof.
> 
> This being net.puzzle, I won't post the answer for a
> while.  If those who have heard this before would hold
> off on responding for a few days, that would give
> others a chance to figure it out on their own.  Thanks.

Sorry to disillusion you but the proof was not new. It had been known 
since antiquity. The program simply observed that the triangle was congruent
to its mirror image and hence concluded that the base angles were equal.
However, it was not a 'new' discovery.

Bob Silverman  (they call me Mr. 9)


By the way... an interesting problem is that of proving that the angle
trisectors of any triangle meet at three points in the interior and that
those three points form an equilateral triangle.