you're moving into your new apartment, and you're trying to bring your
sofa. The problem is, the hallway turns and you have to fit your sofa
around a corner. If it's a small sofa, that might not be a problem, but a
really big sofa is sure to get stuck. If you're a mathematician, you
ask yourself: What's the largest sofa you could possibly fit around the
corner? It doesn't have to be a rectangular sofa either, it can be any
This is the essence of the moving sofa problem.
Here are the specifics: the whole problem is in two dimensions, the
corner is a 90-degree angle, and the width of the corridor is 1. What is
the largest two-dimensional area that can fit around the corner?
largest area that can fit around a corner is called—I kid you not—the
sofa constant. Nobody knows for sure how big it is, but we have some
pretty big sofas that do work, so we know it has to be at least as big
as them. We also have some sofas that don't work, so it has to be
smaller than those. All together, we know the sofa constant has to be
between 2.2195 and 2.8284.