Futurama is the property of 20th Century Fox, and Comedy Central and Matt Groening in some complicated way I don't understand. Clips in this video fall under fair use for review, commentary and educational use. Again, I don't really understand. The Prisoner of Benda first aired on the 19th of August 2010. For more information on this episode see theinfosphere.org For a screenshot of the theorem see pool.theinfosphere.org For more information on the maths of Futurama see mathsci.appstate.edu Click here for my introduction to Group Theory www.youtube.com Let Fry, Zoidberg, the Professor, Washbucket, Hermes, Bender, Leela, the Emperor, and Amy be the initial set of people swapping minds. Then the various swapping of bodies gives the permutation \pi where \pi = (ap)(ab)(pl)(aw)(fz)(ew)(hl) = (fz)(ahlpbew) By Keeler's Inversion Theorem we can return the swapees to their original bodies by introducing two new people, namely Sweet Clyde and Bubblegum Tate, and swapping bodies via the permutation \sigma, where; \sigma = (fs)(zt)(zs)(ft)(ps)(wt)(ls)(et)(hs)(bt)(as)(pt)(ws) and \pi . \sigma = 1 This is a total of 13 body swaps to return people back to normal. In this case we can reduce the total number of body swaps to 9, and exclude the addition of two extra people, by letting \sigma be a different permutation, namely; \sigma = (pf)(wz)(lf)(ez)(hf)(bz)(af)(pz)(wf) where \pi . \sigma = 1 as required.
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