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

For recent (2022) progress see A Numerical Approach for Analysing the Moving Sofa Problem Symmetry, Volume 14, Issue 7.