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On moving a sofa around a corner
I just thought it was a cool title for a paper (if anyone has read it, let me know if it is any good):
in Geometriae Dedicata, Volume 42, Number 3, June 1992 Joseph L. Gerver
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.