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Math Help - Affine vs. Euclidean geometry.

  1. #1
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    Affine vs. Euclidean geometry.

    Give an example of each, or say why no example exists.

    1) A Euclidean transformation that is not affine

    2) An affine transformation that is not Euclidean

    3) A transformation that is both Euclidean and affine

    4) A transformation that is 1-1, but not Euclidean nor affine

    My attempt

    1) This does not exist since ever Euclidean transformation of R^2 is an affine trans. since all orthogonal matrices are invertible

    2) I know one exists, but am having trouble coming up with one. Do I just make the matrix A not be orthogonal, but still be invertible?

    3) Here we can just take any Euclidean transformation since it will automatically be affine. So I can just give an such?

    4) I am not sure here...do I just take the matrix to be any non-orthogonal, non-invertible matrix?







    NEVER MIND, got it!
    Last edited by zhupolongjoe; September 30th 2010 at 02:25 AM. Reason: solved
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  2. #2
    MHF Contributor
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    I believe there is a way to mark a thread as solved so that it shows in the list of threads.
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