
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 wellknown 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

