*N.B. A detailed on-line essay by S. Finch
was the starting point for this entry.*

What is the sofa of greatest Area which can be moved around a right-angled hallway of unit width?
Hammersley (Croft *et al. *1994) showed that

(1) |

(2) |

(3) |

(4) |

(5) |

(6) | |||

(7) | |||

(8) | |||

(9) |

Now define

(10) |

(11) | |||

(12) | |||

(13) |

Finally, define the functions

(14) | |||

(15) | |||

(16) |

The Area of the optimal sofa is given by

(17) |

**References**

Croft, H. T.; Falconer, K. J.; and Guy, R. K. *Unsolved Problems in Geometry.*
New York: Springer-Verlag, 1994.

Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/sofa/sofa.html

Gerver, J. L. ``On Moving a Sofa Around a Corner.'' *Geometriae Dedicata* **42**, 267-283, 1992.

Stewart, I. *Another Fine Math You've Got Me Into....* New York: W. H. Freeman, 1992.

© 1996-9

1999-05-26