From: "Steve Mayer" Subject: Re: Proof of a theorem in geometry by Martin Gardner Date: Wed, 16 Aug 2000 20:26:31 +0100 Newsgroups: sci.math Summary: [missing] Would it be the Dot Conjecture in Simon Singh's book "Fermat's Last Theorem"? He says it was an unsolved problem for a long time but the proof involves "a minimal amount of mathematical knowledge mixed with a little extra cunning". However, he doesn't say who proved it or mention Martin Gardner. The Dot conjecture says: "It is impossible to draw a dot diagram such that every line has at least three dots on it, excluding the diagram where all dots are on the same line." Clearly Simon Singh has used a simple version (so dots instead of points etc) for the book's audience. The proof is two (small) pages long but involves diagrams which are tricky to draw here. If you can't get hold of the book and it is the result you are thinking of I'll see what I can do. Steve Mayer mayer@dial.pipex.com "Peter Yu" wrote in message news:3999171f.0@scctn03.sp.edu.sg... > There was a proof of a theorem in geometry by Martin Gardner. It was about > lines passing through points. The postulate was formed long ago and it was > Martin who proved it in a moment of "Aha". > > It was to inspire people with an interest in maths that difficult problem > could be solved simply. > > Can some one point me to what that theorem was and the proof. > > > > Thanks a lot. ============================================================================== From: israel@math.ubc.ca (Robert Israel) Subject: Re: Proof of a theorem in geometry by Martin Gardner Date: 16 Aug 2000 23:08:48 GMT Newsgroups: sci.math In article <8neq1e$sk9$1@newsg3.svr.pol.co.uk>, Steve Mayer wrote: >Would it be the Dot Conjecture in Simon Singh's book "Fermat's Last >Theorem"? He says it was an unsolved problem for a long time but the proof >involves "a minimal amount of mathematical knowledge mixed with a little >extra cunning". However, he doesn't say who proved it or mention Martin >Gardner. >The Dot conjecture says: >"It is impossible to draw a dot diagram such that every line has at least >three dots on it, excluding the diagram where all dots are on the same >line." This is a famous problem of Sylvester. See http://www.ics.uci.edu/~eppstein/junkyard/sylvester.html for a discussion of this in sci.math back in 1990. Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada V6T 1Z2 ============================================================================== From: John Robertson Subject: Re: Seeking proofs Date: Sun, 20 Aug 2000 14:52:47 GMT Newsgroups: sci.math To: yerachmeel@aol.com Summary: [missing] In article <20000817222049.28602.00000079@ng-fj1.aol.com>, yerachmeel@aol.com (Yerachmeel) wrote: > Can anyone refer me to the complete > proofs of the following: > The Dot conjecture : It is impossible to > draw a dot diagram such that every line has > at least three dots on it, excluding the diagram > where all dots are on the same line. Attributed > to Martin Gardner. See Martin Aigner and Gunter Ziegler, Proofs from THE BOOK, Springer, 1999, Chapter 8, pages 45 to 50. This has a proof, and some historical discussion. I would be surprised if Martin Gardner independently proved this, although he might well have written about it. John Robertson Sent via Deja.com http://www.deja.com/ Before you buy.