Demystifying Science: What is the ‘moving sofa problem’?

It is a deceptively simple question that is comprehensible even to a child: What is the largest sofa that can pivot around an L-shaped hallway corner without lifting, squishing or tilting it? Although it still seems easy to solve, the problem has foxed math sleuths for more than 50 years. That’s because the challenge for mathematicians is both finding the largest sofa and proving it to be the largest. Without formal proof, it’s always possible someone will come along with a better solution. The largest area that will fit around a corner is called the “sofa constant”. It is measured in units where one unit corresponds to the width of the hallway. The largest sofa that can practically achieve the aims of the challenge is the Gerver sofa, which is shaped a bit like an old telephone handset.