
An insomniac's guide to the group theory of mattress flipping (2005) - luckysahaf
http://www.americanscientist.org/issues/pub/group-theory-in-the-bedroom/99999
======
jacobolus
Summary: the dihedral group D2 (isomorphic to the Klein 4 group) needs 2
generators, so you can’t keep performing a single flip/operation on your
mattress and get all viable positions out of it.

For folks trying to learn group theory, I recommend Nathan Carter’s book
_Visual Group Theory_ , an approachable introduction written in conversational
style, full of great pictures (unlike most group theory textbooks, which are
abstract and symbol-heavy).
[http://web.bentley.edu/empl/c/ncarter/vgt/](http://web.bentley.edu/empl/c/ncarter/vgt/)
[http://amzn.com/088385757X](http://amzn.com/088385757X)

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nerdy
Why not just write the name of a season on a corner for each of the 4
configurations and call it a day? The incorrect season on the same side would
be written upside down. If the season is wrong, flip/rotate accordingly.

    
    
      ----------  ----------
    
      ɹǝɯɯnS----  ƃuıɹdS----
    
      ----------  ----------
    
      ----------  ----------
    
      ----Winter  ------Fall
    
      ----------  ----------
    
    

While not flip or rotate, it is a _single operation_ : "Align the current
season to the bottom"

~~~
hammock
But if you are heaviest in the winter, every winter, it will result in uneven
wear :)

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dandelany
If you like this kind of thing, Brian Hayes (the author) has a whole book of
similar mathematical anecdotes/puzzles: [http://www.amazon.com/Group-Theory-
Bedroom-Mathematical-Dive...](http://www.amazon.com/Group-Theory-Bedroom-
Mathematical-Diversions/dp/0809052172)

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count_zero
If your mattress has a tag in one corner, it becomes pretty simple to know
which operation to perform next.

If, when facing the headboard, the tag is to your right, rotate; else, flip
(on the roll axis).

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utopkara
Pun Maths: "Mattress multiplication"

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leecarraher
nothing to see here, just a friday afternoon deadline article about the
dihedral group

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spdegabrielle
Brian Hayes always writes great stuff [http://bit-player.org](http://bit-
player.org)

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cecilpl
This post was interesting, though less interesting than I expected based on
the title.

~~~
dang
We changed the title to the subtitle for obvious reasons.

~~~
dragonwriter
Is that really better? On the one hand, it makes it more specific what the
example domain is ("mattress flipping" vs. "the bedroom"), on the other, it
makes it less specific what its being used as an example _of_ ("mathematics"
vs. "group theory".)

It seems to me that the change is a net loss in terms of useful information
about whether this is something you want to click through to.

~~~
dang
Ok, we replaced 'curious mathematics' with 'group theory'.

