Projecting 3-Sphere onto a Plane | Stereographic Projection

[Carol_m]

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

 

[xts]

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.

 

[Carol_m]

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 textbooks 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!

 

[xts]

I want to project every point in the sphere (not only the surface) on a 2D plane

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