
threedimensional 'surface' of multidimensional 'sphere'
Posted:
Jan 11, 2014 11:46 AM


Hi,
I may have posted this question either three months or three years ago. I am trying to fill in the background of a scifi 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 threedimensional 'surface' of a multidimensional 'sphere' be?
For example
x**2 + y**2 + z**2 = r**2
is the equation of a 'twodimensional surface' of a threedimensional 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' threedimensional space?
I'm assuming the 'sphere' is at the 'center' of the multidimensional space.
Thx & Regards,
Ken

