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Torus used to model 4D rotation

  1. Nov 4, 2015 #1
    A torus can be used to model rotations of a sphere in 4 dimensions. Such rotations have two planes of rotation at right angles to one another. So one rotation plane corresponds to rotation around the major axis of the torus, and the other rotation plane to rotation around the minor axis. Viola, four dimensions. Neat, huh?

    Take a point (a,b,c,d). The major axis is then a^2+b^2 and the minor axis is c^2+d^2. That point then travels around the surface of the torus with one period of rotation around the major axis and the other around the minor.
     
  2. jcsd
  3. Nov 9, 2015 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
  4. Nov 19, 2015 #3
    If one is willing to accept nonrigid rotations then it is possible to have a real world object that rotates in two planes with two entirely different periods of rotation. A torus can rotate this way, around the major axis and the minor axis. Such things are sold as toys. I used to have one.

    Given infinite flexibility I'm pretty sure it is theoretically possible to have any number of planes of rotation for a real world object. But an endlessly stretchable material is highly unrealistic. Can anyone figure out a way to have more than two planes of rotation for a real-world object of limited flexibility?
     
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