Mathematicians have solved the ‘moving sofa problem’, which asks for the largest two-dimensional shape that can be manoeuvred through an L-shaped hallway without getting stuck at a corner.
The solution, a shape proposed in the 1990s by Rutgers University’s Joseph Gerver, was thought to be the answer but mathematicians were unable to prove it until now.
While the shape is defined in such a way that its area can’t be expressed in terms of known quantities, it is the optimal solution to the simple problem.
The solution required combining techniques from disparate areas of mathematics to make a problem tractable, without the need for computer assistance.
Proving the sofa to be the largest possible shape that could navigate the hallway is hoped to provide a new approach to optimisation problems.
