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Topic: three-dimensional 'surface' of multi-dimensional 'sphere'
Replies: 6   Last Post: Jan 23, 2014 5:42 PM

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ken quirici

Posts: 332
Registered: 1/29/05
three-dimensional 'surface' of multi-dimensional 'sphere'
Posted: Jan 11, 2014 11:46 AM
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Hi,

I may have posted this question either three months or three years ago. I am trying to
fill in the background of a sci-fi story and this seems an interesting possibility. I am not
a professional mathematician and my math education is almost as old as I am. A Master's
in pure math can cover a multitude of deficiences even if it were recent.

What would the equation of a three-dimensional 'surface' of a multi-dimensional 'sphere'
be?

For example

x**2 + y**2 + z**2 = r**2

is the equation of a 'two-dimensional surface' of a three-dimensional sphere.

Implicit is the other question, what is the minimum number of dimensions for this
object?

Possibly if the dimensions are indicated by x, y, z, a:

x**2 + y**2 + z**2 + a**2 = r**2

but would a 'person' in whatever 'space' this describes perceive it as a
locally 'flat' three-dimensional space?

I'm assuming the 'sphere' is at the 'center' of the multi-dimensional space.

Thx & Regards,

Ken



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