 | ||
The moving sofa problem or sofa problem is a two-dimensional idealisation of real-life furniture-moving problems and asks for the rigid two-dimensional shape of largest area A that can be maneuvered through an L-shaped planar region with legs of unit width. The area A thus obtained is referred to as the sofa constant. The exact value of the sofa constant is an open problem.
Contents
History
The first formal publication was by the Austrian-Canadian mathematician Leo Moser in 1966, although there had been many informal mentions before that date.
Lower and upper bounds
Work has been done on proving that the sofa constant cannot be below or above certain values (lower bounds and upper bounds). One lower bound is
John Hammersley derived a lower bound of
Joseph Gerver found a sofa described by 18 curve sections each taking a smooth analytic form. This further increased the lower bound for the sofa constant to approximately 2.2195.
A computation by Philip Gibbs produced a shape indistinguishable from that of Gerver's sofa giving a value for the area equal to eight significant figures. This is evidence that Gerver's sofa is indeed the best possible but it remains unproven.
Hammersley also found an upper bound on the sofa constant, showing that it is at most
Ambidextrous Sofa
A variant of the Sofa Problem asks the shape of largest area that can go round both left and right 90 degree corners in a corridor of unit width. A lower bound of area approximately 1.64495521 has been described by Dan Romik