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Gibbs's computational approach is really interesting [1]. Keep the sofa still and move the corridor, and the optimal sofa shape is the intersection of all (well n, since it's a numerical approximation) the corridor shapes as they sweep around.

[1] https://www.researchgate.net/publication/311900489_A_Computa...

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> ...describing sofas in terms of the translations and rotations as a function of time is by now a standard way of thinking about the moving sofa problem, and has been used in the attack on the problem by Joseph Gerver in his paper from 1992, and in my own recent paper, where among other thing I made precise your suggested notion of describing the sofa shape that results from the continuous intersection of corridors rotating and translating over time. See my paper (available here: https://www.math.ucdavis.edu/~romik/data/uploads/papers/sofa...), and especially Theorem 1 in section 2.

Dan Romik

That link does not work for me, but this may be better : https://www.math.ucdavis.edu/~romik/movingsofa/

That is a different article. My link to Gibbs's article came from Wikipedia, but your link points to another copy: http://vixra.org/pdf/1411.0038v2.pdf

Maybe that one will work for you.

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