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On moving a sofa around a corner


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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  1. 1.

    Conway, J. H., private communication.

  2. 2.

    Croft, H. T., Fowler, K. J. and Guy, R. K.,Unsolved Problems in Geometry, Springer-Verlag, New York, 1991, pp. 171–172.

    Google Scholar 

  3. 3.

    Guy, R. K., ‘Research problems’,Amer. Math. Monthly 84 (1977), 811.

    MathSciNet  Google Scholar 

  4. 4.

    Hammersley, J. M., ‘On the enfeeblement of mathematical skills by ldModern Mathematicsrd and by similar soft intellectural trash in schools and universities’,Bull. Inst. Math. Appl. 4 (1968), 66–85.

    Google Scholar 

  5. 5.

    Moser, L., ‘Problem 66–11: Moving furniture through a hallway’,SIAM Rev. 8 (1966), 381.

    Google Scholar 

  6. 6.

    Odlyzko, A. M., private communication.

  7. 7.

    Wagner, N.R., ‘The sofa problem’,Amer. Math. Monthly 83 (1976), 188–189.

    MATH  MathSciNet  Google Scholar 

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Gerver, J.L. On moving a sofa around a corner. Geom Dedicata 42, 267–283 (1992).

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  • Maximum Area
  • Unique Region
  • Unit Width