Here is how someone scientifically views the process of mattress flipping.

To make sense of all this turning and flipping, the first thing we need is some clear notation. A mattress can be rotated around any of three orthogonal axes. I could label the axes x, y and z, but I’d just forget which is which, so it seems better to adopt the terminology of aviation. If you think of a mattress as an airplane flying toward the headboard of the bed, then the three axes are designated roll, pitch and yaw as shown in the illustration to the right. The roll axis is parallel to the longest dimension of the mattress, the pitch axis runs along the next-longest dimension, and the yaw axis passes through the shortest dimension.

Turning the mattress by 180 degrees around any one of these three axes is a symmetry operation: If you start with the mattress properly installed on the bed and then apply one of these actions, you return to another state where the mattress fits the bed frame correctly. Assuming that the various surfaces of the mattress are not labeled in any way, the states before and after the symmetry operation are indistinguishable. Note that no rotation through an angle smaller than a half turn has this property; despite the advice of Phyl’s Furniture Facts, a quarter turn around any axis leaves the mattress in a decidedly awkward position. And for a mattress that has the usual, rectangular, shape (technically, it’s called an orthotope), there are no other symmetry axes. If you were to try making a half turn around one of the diagonals, you’d be left with a very catterwumpus bed.

I did not realize it can be that complicated!

Tags: MATTRESS News, mattress-flipping

This entry was posted on Friday, May 18th, 2007 at 3:00 pm and is filed under MATTRESS News.
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