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Reflection of a 2-d shape about some line

  1. Mar 4, 2010 #1
    I've noticed the the reflection of a 2-d shape about some line is the same as rotating it by 180 degrees about that line, where it rotates through the third dimension. Does this generalise to higher dimensions? I hope it's clear what I mean here.
     
  2. jcsd
  3. Mar 5, 2010 #2

    Ben Niehoff

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    Re: Reflection/Rotation

    Yes, it generalizes exactly as you would expect. Reflecting in a plane in 3D is the same as rotating about that plane in 4D, etc.
     
  4. Mar 5, 2010 #3
    Re: Reflection/Rotation

    Not only that, but any rotation can be obtained by two successive reflexions, through different lines. See if you can prove that.
     
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