An insomniac's guide to the group theory of mattress flipping (2005)

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://amzn.com/088385757X

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"

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...

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).

Pun Maths: "Mattress multiplication"

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

Brian Hayes always writes great stuff http://bit-player.org

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