5 ms·
An insomniac's guide to the group theory of mattress flipping (2005)
- deleted 10y ago[deleted]
- nerdy 10y agoWhy 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"
- dahdum 10y agoA bit different, but my first thought was to use even/odd and the date. Odd Month / Quarter = flip head to end Even Month / Quarter = flip side to side That would be four states of the mattress per year, at the cost of remembering the rule.
- hammock 10y agoBut if you are heaviest in the winter, every winter, it will result in uneven wear :)
- sopooneo 10y agoI have seen almost exactly this on hotel mattresses. But it had three months in each spot instead of the season. "Jan/Feb/March" in one spot then "Apr/May/Jun" in the next, etc.
- jacobolus 10y agoSummary: 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
- cecilpl 10y agoThis post was interesting, though less interesting than I expected based on the title.
- dang 10y agoWe changed the title to the subtitle for obvious reasons.
- dragonwriter 10y agoIs 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 10y agoOk, we replaced 'curious mathematics' with 'group theory'.
- deleted 10y ago[deleted]
- count_zero 10y agoIf 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).
- spdegabrielle 10y agoBrian Hayes always writes great stuff http://bit-player.org http://bit-player.org
- utopkara 10y agoPun Maths: "Mattress multiplication"
- leecarraher 10y agonothing to see here, just a friday afternoon deadline article about the dihedral group
- dandelany 10y agoIf 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-Diversions/dp/0809052172 http://www.amazon.com/Group-Theory-Bedroom-Mathematical-Dive...