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another sum exlusive

Issue 16 - Dec 2005

The Maths Of Mattress Flipping

mattress flipping Apparently mattress flipping is a chore that confuses many people, as they never really know if they are 'doing it right' But now we have the maths!...Or do we?

Companies that manufacture mattresses, generally recommend that you flip or turn your mattress every so often so that it wears evenly and you get the longest possible life from it.

When broken down to a formulaic exercise, it becomes apparent that there are in fact only four possible combinations of head and foot, top and bottom mattress flipping that can be performed to ensure even wearing.

In the ideal world there would be a maneuver you could execute each time you flip your mattress which after four repetitions would mean that all four combinations would have been used. Brian Hayes, writing in the September-October 2005 issue of American Scientist calls this mythical combination a mathematical 'golden rule'. Unfortunately for the world's house wives / husbands he also proclaims that no such golden rule exists.

mattress flipping 2Mathematically, there are four ways to rotate a mattress so that it ends up aligned with the bed. Hayes uses the symbols I for the Identity rotation (wait until next week) and R, P, Y for the nautical terms Roll, Pitch and Yaw. Image courtesy Brian Hayes.

His argument runs as follows: no matter how creatively you manipulate your mattress, once it's back on the bed you will have performed one of the four operations I, R, P, Y shown in the figure. Each of these operations has the property that if you repeat it, you end up where you started. So you will have missed two of the configurations.


Article:Tony Phillips' Take on Math in the Media

Maths In Media Website


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Sudoku Saves Maths?

The 'Leap Second'

Maths Olympics

The Maths Of Mattress Flipping

Sum Fun - SUDOKU

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