Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

 Search Thread: Advanced Search

 Messages: [ Previous | Next ]
 Chan-Ho Suh Posts: 425 Registered: 12/10/04
Re: Hex Win Proof?
Posted: Mar 23, 2004 10:08 PM
 Plain Text Reply

In article <c3p0bk\$2fl7ms\$1@athena.ex.ac.uk>, Robin Chapman
<rjc@ivorynospamtower.freeserve.co.uk> wrote:

> Torben ÃÂÃÂÃÂÃÂ¸ÃÂÃÂidius Mogensen wrote:
>

> >
> > Indeed, if we want to prove it to a mathematician who does not already
> > accept the intermediate value theorem (of which the intersection
> > property is a simple consequence).

>
> Is it?
>
> Now I presume this "intersection property" can be paraphrased as
> "a path with endpoints at two opposite vertices of a square with
> all other points in the interior of the square must meet a path
> with endpoints at the other two vertices of the square with
> all other points in the interior of there square".
>
> That's a simple consequence of the intermediate value theorem, is it?
>
> I must be stupid, since the only way I can see to prove that is
> using the Jordan Curve Theorem. :-(

I don't think you're being stupid, unless I'm being stupid also :-)

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.

I'm very skeptical of this, because if you could show the paths must
intersect with the intermediate value theorem, then I think you have a
proof of Jordan separation with just a little extra work. So this
would be a much simpler proof than I've ever seen of that.

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

© The Math Forum at NCTM 1994-2018. All Rights Reserved.