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Topic: Hex Win Proof?
Replies: 41   Last Post: Mar 24, 2004 6:39 PM

 Messages: [ Previous | Next ]
 Tim Smith Posts: 1,142 Registered: 12/6/04
Re: Hex Win Proof?
Posted: Mar 24, 2004 5:15 AM

In article <c3rhkr\$289gvb\$2@athena.ex.ac.uk>, Robin Chapman wrote:
>> I can't see a way to prove this without Jordan separation. It's not just
>> a matter of the intermediate value theorem. If one path can be
>> straightened out, then one can apply the intermediate value theorem, but
>> saying that you can straighten out a path is essentially the content of
>> the Jordan curve theorem.

>
> More than that --- it's almost the Schoenflies theorem. On the other
> hand, if one is dealing with a path on a lattice, like we are doing here,
> then one can do the straightening stepwise and end us with a nice "theta"
> shape which we can apply the IVT to.

I'd be suspicious of any use of well-known curve theorems without going over
their proofs and making sure they apply to paths on the Hex board, because a
path on the Hex board can, without intersecting itself, close off a region
of the board.

--
--Tim Smith

Date Subject Author
3/18/04 Bill Taylor
3/18/04 Tim Brauch
3/19/04 Brian Chandler
3/19/04 Jonathan Welton
3/19/04 Tim Brauch
3/19/04 Richard Henry
3/20/04 Chan-Ho Suh
3/21/04 Arthur J. O'Dwyer
3/19/04 Bob Harris
3/19/04 Tim Smith
3/19/04 Dvd Avins
3/20/04 Nate Smith
3/20/04 Chan-Ho Suh
3/20/04 G. A. Edgar
3/19/04 Richard Henry
3/19/04 Steven Meyers
3/20/04 Nate Smith
3/20/04 Larry Hammick
3/20/04 Tim Smith
3/21/04 Steven Meyers
3/22/04 Torben Mogensen
3/22/04 Chan-Ho Suh
3/22/04 Torben Mogensen
3/22/04 Chan-Ho Suh
3/23/04 Torben Mogensen
3/23/04 Robin Chapman
3/23/04 Chan-Ho Suh
3/24/04 Robin Chapman
3/24/04 Tim Smith
3/24/04 Robin Chapman
3/24/04 Tim Smith
3/24/04 Jon Haugsand
3/22/04 Andrzej Kolowski
3/23/04 Alexander Malkis
3/23/04 Chan-Ho Suh
3/23/04 Dr. Eric Wingler
3/24/04 Danny Purvis
3/24/04 Danny Purvis