gwyn@brl-tgr.ARPA (Doug Gwyn <gwyn>) (11/15/85)
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.
bs@faron.UUCP (Robert D. Silverman) (11/17/85)
> 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.
tan@ihlpg.UUCP (Bill Tanenbaum) (11/19/85)
> 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. ------ That's easy. Just use Morley's theorem!-)-)-) -- Bill Tanenbaum - AT&T Bell Labs - Naperville IL ihnp4!ihlpg!tan
hopp@nbs-amrf.UUCP (Ted Hopp) (11/23/85)
> > 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