From plane to hyperplane in high dimension

  1. Hello All,

    It's rather a simple question for advanced people.

    Consider a 3D Euclidean space: if one is given 2 points, a line can be build that goes through the points; for 3 points -- there is a plane.

    For 4D space: a line goes through 2 points and a hyperplane through 4 points.

    The question -- what's the name for the object that can be build with given 3 points in 4D space? And more generally, for (N-i) points, 1<i<N-2, in N-dimensional space?

    Where can I look for more info on this topic.

    Thanks in advance!
  2. jcsd
  3. micromass

    micromass 20,073
    Staff Emeritus
    Science Advisor
    Education Advisor

    Well, through n points goes exactly one (n-1)-dimensional affine subspace. Maybe that's what you're looking for?
  4. Thank you! I'm looking for a way to find distance from a point to an object (line, hyperplane, etc) that goes through n points.. I've just done a search on a distance from a point to an affine subspace and it seems that it's not a trivial topic (at least not as simple as in the case of a line or hyperplane).

    Would there be a suggestion in which direction to go?
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