The Direction Claim:Seen from the top, the path always moves SW-NE or NE-SW on the bottom and SE-NW or NW-SE on the top. Proof: At the start the path is on the bottom and moving SW-NE. From the Two Corners Claim, when the path climbs the walls, it ends up on the other wall of the box and so the direction of the path on the top will be SE-NW and appear perpendicular (looking down) to the path on the bottom. This pattern continues. The paths on the bottom are always perpendicular to the paths on the top, establishing the claim. |