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On moving a sofa around a corner

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Abstract

A necessary condition is given for a region of the plane to have the greatest possible area of any region able to move around a right-angled corner in a hallway of unit width. A region is constructed, with area 2.2195... and bounded by 18 analytic pieces, which satisfies this condition. It is conjectured that this is the unique region of maximum area.

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Gerver, J.L. On moving a sofa around a corner. Geom Dedicata 42, 267–283 (1992). https://doi.org/10.1007/BF02414066

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  • DOI: https://doi.org/10.1007/BF02414066

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