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

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 Tim Smith Posts: 1,142 Registered: 12/6/04
Re: Hex Win Proof?
Posted: Mar 24, 2004 6:39 PM
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In article <c3ropb\$2fmjnb\$1@athena.ex.ac.uk>, Robin Chapman wrote:
>> 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.

>
> I don't see that this is relevant. One replaces the path of pieces on the
> hex board by a curve built from line segments joining the centres of the
> hexagons in question. These paths are between vertices

Yeah, you're right. For what we need here, that's going in the "safe"
direction. That is, take a curve derived from the placement of hexes, and
that curve has to satisfy all the general theorems about 2D curves.

The "unsafe" direction would be taking a general property of 2D curves, and
trying to apply that property to paths of hexes. E.g., a simple closed
curve has an inside and an outside, and the inside is connected. However, a
simple closed path of hexes doesn't necessarily have an inside, and if it
does, the inside is not necessarily connected--it can be pinched off into
multiple disconnected regions.

--
--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 Glenn C. Rhoads
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
3/20/04 Glenn C. Rhoads
3/20/04 Glenn C. Rhoads
3/21/04 Steven Meyers
3/22/04 Glenn C. Rhoads
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

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