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Homework Help: The Group of Rigid Motions

  1. Dec 2, 2003 #1

    It will be easier to first post the question:

    [Note: there are many parts to the original question. This is only part of it].

    I am not sure how to proceed here. Firstly I know that the above function is a translation. I also know that if delta has an infinite order then deltan cannot equal the identity for any n which is an element of Z.

    Now I can see that x deltan = (x+n, (-y)n) and that deltan will never return to (x,y).

    But I am not sure how to prove this. If anything is unclear, please ask and I will try to clarify my question.

    Do I first prove by induction on n that

    x deltan = x + n for all x, n > 0

    and if n > 0 then x + n is not equal to x so deltan does not equal the identity?

    Any help is appreciated. Thankyou.
  2. jcsd
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