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    I am studying transformations on the two and three dimensional cases. I have seen theorems with proof of maps preserving unit area and perimeter on the 3 to infinity case, but I'm looking for a theorem with proof of it just in the 2 dimensional case and just in the 3 dimensional case.
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    (Original post by JakeJohnJones123)
    I am studying transformations on the two and three dimensional cases. I have seen theorems with proof of maps preserving unit area and perimeter on the 3 to infinity case, but I'm looking for a theorem with proof of it just in the 2 dimensional case and just in the 3 dimensional case.
    Wouldn't such a map need to be an isometry (at least in the 2d case)? In which are you asking for a proof of such a result?
 
 
 

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