How to tell if it will fit around the corner

Before you carry that sofa up the stairs, you might want to take out some paper and a pencil (or, these days, a calculator) and figure out if you're going to be able to get it around the right-angled corner on the second floor. Here's how to tell.

First, trudge on up to the second floor. Now, skip lightly down the stairs[1], get your tape measure, and return to the mezzanine. Next, measure the width of the corridor on both sides of the corner; call these widths x and y. For example,

   ---------------------+
       2                |
   -------------+       |
                |       |
                |       |
                |   4   |
                |       |

Now, evaluate the expression (x^2/3 + y^2/3)^3/2 This value is the length of the longest rigid object that you can get around the corner[2]. In the example, that would be about 8 and one third.

It may be helpful to remember that

n^ab = n^ab thus, n^2/3 is the cube root of the square of n (or the square of the cube root of n, if you prefer).

But remember also, as all who have moved know, you can also stand the sofa on its end.

[1] You may also slide down the bannister, if you wish.

[2] Don't forget though, this is actually the length of the longest line segment that can be gotten around the corner; your sofa has a non-zero width, also!