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Science Forum

  1. 27 Aug '08 19:36
    I know that in mathematics, Group Theory is the formal study of symmetry. However, having done quite a lot of group theory I am left with this question:

    How?

    I understand that the dihedral groups, and subgroups thereof, represent symmetries wonderfully. But, for instance, what would be represented by the Symmetric groups? would it be some n-dimensional object (where the symmetric group is S_n)?
  2. Standard member flexmore
    Quack Quack Quack !
    28 Aug '08 02:21 / 1 edit
    Originally posted by Swlabr
    ... would it be some n-dimensional object (where the symmetric group is S_n)?
    You might have some grasp of group theory ... but your simple arithmetic has slipped just a little:

    S3 is like a 2d triangle,
    and
    S4 is like a 3d cube.
  3. Standard member flexmore
    Quack Quack Quack !
    28 Aug '08 04:48
    You could be meaning: Sn is symmetric in the same way as a regular (n-1) simplex.
  4. 28 Aug '08 13:39
    Originally posted by flexmore
    You might have some grasp of group theory ... but your simple arithmetic has slipped just a little:

    S3 is like a 2d triangle,
    and
    S4 is like a 3d cube.
    Numbers: a mathematicians greatest weakness.
  5. 28 Aug '08 13:44
    Originally posted by flexmore
    You might have some grasp of group theory ... but your simple arithmetic has slipped just a little:

    S3 is like a 2d triangle,
    and
    S4 is like a 3d cube.
    Yes-that makes sense. Thanks for that.