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Hypersphere projection

  1. Jul 15, 2011 #1
    Hello,

    Is it possible to project a hypersphere (a 3-sphere) onto a plane? is this possible using stereographic projection?

    Please, if this is possible I would appreciate a nice explain me about how to do it.

    Thank you!

    Carol
     
  2. jcsd
  3. Jul 15, 2011 #2

    xts

    User Avatar

    Of course, not!
    You may stereographically project the 2-dimensional sphere (bended in 3 dims) on 2-dimensional flat plane. Similiraly, you could develop some projections of 3-D hypershere, bended in 4th dim onto flat 3-D space. But not on 2-D one.

    You may think about projecting it first on flat 3D Euclidean space, and then use some common method of visualisation to present it as a 2-D picture.
     
  4. Jul 18, 2011 #3
    Hello xts,

    Thank you for your reply and sorry if I am being too naive but I do not follow your answer. Could you please explain me a bit more? (sorry but this is not my background)

    From what I have read in text books I know that you can project the surface of a sphere in a 2-D plane, my problem is that I want to project every point in the sphere (not only the surface) on a 2D plane, that's why my question was about hypersphere projection (but maybe I am also confuse about this??).

    If you can help me about this I would really appreciate it and sorry again if I am asking the obvious.

    Thank you!
     
  5. Jul 18, 2011 #4

    xts

    User Avatar

    Then you must project infinite number of points (some line segment) of your sphere into a single point on your plane.
     
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