Date: Mar 24, 2004 5:15 AM
Author: Tim Smith
Subject: Re: Hex Win Proof?

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