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# Group Theory in the Bedroom

An insomniac's guide to the curious mathematics of mattress flipping

Sleepers Awake

In the morning, when I Googled "mattress flipping," I learned that I'm not the only one who's been obsessing about this silly business. Linda Cobb, The Queen of Clean®, recommends flipping on a seasonal schedule—side-to-side in spring and fall, and end-over-end in summer and winter. Or maybe it's the other way around; I forget. A Web site called eHow, which promises "Clear Instructions on How To Do (just about) Everything" offers the following counsel: "Rotate your mattress twice a year, or more often if instructed by the manufacturer. Flip it over completely after the first six months. Then, after another six months, flip it over and turn it so that the head is at the foot of the bed." Is that clear? What would it mean to flip it over incompletely? And what's the difference, exactly, between rotating, flipping and turning? Does the final instruction to flip and turn do anything that couldn't be achieved with a single motion?

Another Web page, Phyl's Furniture Facts, takes on the task of defining some of this terminology: "Flipping means to turn it over while rotating means to make a 1/4 turn of the mattress while it lies flat on the bed." (I tried the quarter turn, but it didn't look very comfortable.)

Versions of the illustration reproduced at right appear on dozens of Web sites. When I first saw this diagram, I thought for a fleeting moment that I had found my golden rule. A quarter turn, a flip, another quarter turn—"AND THERE YOU ARE.... Turned Over and End to End as well!" Maybe this was the magic formula. But no: A quick experiment with a small model of a mattress—I used a paperback book—showed that the elaborate sequence of operations in the diagram has exactly the same effect as a half turn end-over-end. (But the more-complicated procedure may be worth following anyway, especially in a room with a low ceiling.)

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