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From plane to hyperplane in high dimension

by uwowizard
Tags: dimension, hyperplane, plane
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uwowizard
#1
Aug19-11, 04:29 PM
P: 14
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!
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micromass
#2
Aug19-11, 04:31 PM
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P: 18,299
Well, through n points goes exactly one (n-1)-dimensional affine subspace. Maybe that's what you're looking for?
uwowizard
#3
Aug19-11, 04:41 PM
P: 14
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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