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Thread: What is a surface in Maths and/or Physics?

  1. #1 What is a surface in Maths and/or Physics? 
    Junior Member
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    I have learned in another forum that a ID lines can be a surface on a 2D plane and a 2D plane can be a surface on a 3D Volume.

    Can this be generalized mathematically as we introduce more (higher) dimensions?

    Is it the case (as it seems to me to be true in the examples I have given) that when we set one of the dimensional variables to a constant that what we have is a surface ?(I think they may be referred to as hypersurfaces in higher dimensions)

    By setting one of the dimensional variables to a constant (decreasing its value range to smaller and smaller quantities in the same way as is done in Calculus *,do we effectively transform the n-Dimensional model to a n-1 Dimensional model and create a (hyper)surface that "straddles" the 2 models?

    *ie as a limit
    Last edited by geordief; 11-16-2017 at 02:29 PM.
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  2. #2  
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    Quote Originally Posted by geordief View Post
    I have learned in another forum that a ID lines can be a surface on a 2D plane and a 2D plane can be a surface on a 3D Volume.

    Can this be generalized mathematically as we introduce more (higher) dimensions?

    Is it the case (as it seems to me to be true in the examples I have given) that when we set one of the dimensional variables to a constant that what we have is a surface ?(I think they may be referred to as hypersurfaces in higher dimensions)

    By setting one of the dimensional variables to a constant (decreasing its value range to smaller and smaller quantities in the same way as is done in Calculus *,do we effectively transform the n-Dimensional model to a n-1 Dimensional model and create a (hyper)surface that "straddles" the 2 models?

    *ie as a limit
    Here is the rigorous mathematical treatment of the concept called "embedding".
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