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Math Help - define a map

  1. #1
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    define a map

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    Last edited by yellow4321; March 6th 2008 at 06:10 AM.
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  2. #2
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    Quote Originally Posted by yellow4321 View Post
    this question has been bugging me:
    how could i define a map f:Complex--->Complex (complex plane)
    that is a glide reflection
    i have ideas but struggling to put show as a map?
    Hint: What is a glide reflection? It is a composition of a rotation and a reflection.
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  3. #3
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    Last edited by yellow4321; March 6th 2008 at 06:10 AM.
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  4. #4
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    Quote Originally Posted by yellow4321 View Post
    where r= reflection and t=translation

    (t o r) perhaps but when i have it for the complex plane would i say r=reflection in some line x=3 perhaps, and translation by i or something?
    Note the function f(z) = \bar z is the reflection of a complex number through the x-axis. And g(z) = z+1 is a translation of a number by 1 unit to the right. Hence  f\circ g = \bar z + 1 is a glide reflection.
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