Sunday, February 11, 2018

[nuyxqahp] Sofa maze

Depict a solution to Moser's Moving Sofa Problem, e.g., the Gerver Sofa, moving around a No Left Turn maze.

Subtleties: is U-turn permitted?  If so, the sofa changes parity in what type of turn it can make.  If the maze has infinitely thin walls, then I think the Gerver Sofa cannot navigate hairpins, two right turns immediately in a row.  This suggests a new problem, the largest sofa which can make that turn.

Romik's ambidextrous sofa can travel through an ordinary maze with no turn restrictions, though it may still have problems with hairpins.

Moser's Moving Sofa Problem can easily be generalized to other angles (e.g., a maze using an underlying equilateral triangular lattice), and probably more dimensions.

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