Reflection of a 2-d shape about some line

  • Thread starter madness
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  • #1
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Main Question or Discussion Point

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.
 

Answers and Replies

  • #2
Ben Niehoff
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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.
 
  • #3
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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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