A bit like the three body problem, I guess. The problem seems simple because it’s just four walls, but think how complicated the constraints are once you have a

A bit like the three body problem, I guess. The problem seems simple because it’s just four walls, but think how complicated the constraints are once you have an arbitrary shaped sofa: you shave a tiny bit off one corner, and now you can translate the sofa in one axis a little bit or rotate it a little bit. But all the other points in the sofa are potentially limiting that movement, in complex ways because they might be curved. You get stuck, so you shave a tiny bit off somewhere else and suddenly all the constraints have changed again depending on the cut you made. The optimal shape is rather elegant, I think, because it’s basically the half-donut shape you’d expect but with some very limited perturbations that gain a tiny bit of area during key transitions.