Date: Mar 20, 2004 8:15 AM
Author: G. A. Edgar
Subject: Re: Hex Win Proof?
All related to the fact that the plane is 2-dimensional...
You cannot tile 3-space with small tiles meeting no more than 3 at
a time! But you can in 2-space. With hexagons (as here) or rectangles
arranged like brick-work. Two opposite sides of a square (or
paralellogram) can be separated from each other by a one-dimensional
curve. But this cannot be done for two opposite faces of a cube... You
have to use a 2-dimensional surface to separate it.
G. A. Edgar http://www.math.ohio-state.edu/~edgar/