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From: hopp@nbs-amrf.UUCP (Ted Hopp)
Newsgroups: net.puzzle
Subject: Re: Re: A somewhat different geometry problem
Message-ID: <75@nbs-amrf.UUCP>
Date: Sat, 23-Nov-85 15:03:47 EST
Article-I.D.: nbs-amrf.75
Posted: Sat Nov 23 15:03:47 1985
Date-Received: Thu, 28-Nov-85 03:44:13 EST
References: <2966@brl-tgr.ARPA> <264@Navajo.ARPA> <242@ur-cvsvax.UUCP> <3253@brl-tgr.ARPA> <386@faron.UUCP>
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Organization: National Bureau of Standards
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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.

> 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.

The program was Gelertner's "Geometry Machine", described in his article
in Computers and Thought (Feigenbaum and Feldman, Eds., 1963).  The
discovery was "new" in the sense that Gelertner was not aware of the
proof (which is indeed antique) at the time he wrote the program.  (I
remember reading somewhere about how Gelertner at the time thought the
result was indeed new.)  In other words, the program used knowledge provided
by the author to generate knowledge new to the program's author.  In 1963,
this was quite startling!

-- 

Ted Hopp	{seismo,umcp-cs}!nbs-amrf!hopp