I believe this is technically incorrect, but it errs on safe side. I.e. if the string sweeps through the arc, the box will fit, if it doesn't swing through the

I believe this is technically incorrect, but it errs on safe side. I.e. if the string sweeps through the arc, the box will fit, if it doesn't swing through the arc, there is still a chance that the box will fit. I'm assuming this is what you are referring to by "edge cases". Mathematically this "string theory" (sorry, couldn't help myself) is saying the following: sqrt[ (l/2)^2 + b^2 ] < min(x,y) where l = length of box, b = base of box, and x and y are the respective widths of the two hallways. However, this ignores the fact that the pivot point on the box around the corner can slide as you push the box around the corner. So the pivot point could essentially slide from one end of the box to the other (at some point sliding through the midpoint you are measuring for), which allows a lot more leeway for the box's acceptable dimensions. I worked on this problem a bit this morning, but I don't have my trusty TI-89 calculator to help out. This is actually a calculus problem that I have a difficult time explaining without posting some sketches. Maybe I'll do that in the near future.