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, 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,
| 4 |
Now, evaluate the expression
(x2/3 + y2/3)3/2
This value is the length of the longest rigid object that you can
get around the corner. In the example, that would be about
8 and one third.
It may be helpful to remember that
nab = nab
is the cube root
of the square
(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.
 You may also slide down the bannister, if you wish.
 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!