The moving sofa problem is a well-known unsolved problem in geometry, ﬁrst posed by Leo Moser in 1966, It asks: “What is the planar shape of maximal area that can be moved around a right-angled corner in a hallway of unit width?” We refer to a connected planar shape that can be moved around a corner in a hallway as described in the problem as a moving sofa shape, or simply a moving sofa.
Source : Improved upper bounds in the moving sofa problem
The exact value of the so-called 'sofa constant' is an open problem - although theory and computer assisted calculations suggest that it's between 1.57 and 2.37
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