Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

From plane to hyperplane in high dimension

  1. Aug 19, 2011 #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. Aug 19, 2011 #2
    Well, through n points goes exactly one (n-1)-dimensional affine subspace. Maybe that's what you're looking for?
  4. Aug 19, 2011 #3
    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?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook