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From plane to hyperplane in high dimension 
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#1
Aug1911, 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 (Ni) points, 1<i<N2, in Ndimensional space? Where can I look for more info on this topic. Thanks in advance! 


#2
Aug1911, 04:31 PM

Mentor
P: 18,299

Well, through n points goes exactly one (n1)dimensional affine subspace. Maybe that's what you're looking for?



#3
Aug1911, 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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