A spherical surface in 3D space (x,y,z) with radius (r) is represented as a simple equation.

x^2 + y^2 + z^2 = r^2

The regions within and beyond the surface are undefined.

In order to define the inner region bounded by the surface, assume one more dimension (λ) must be included. A spherical region having a constant surface radius (a) and components (λ,x,y,z) may have an enclosed region defined as;

λ^2 + x^2 + y^2 + z^2 = a^2

λ^2 + r^2 = a^2

Where; a is assumed to be constant

r = 0 and; λ = a represents the center of the spherical region

r = a and; λ = 0 represents the surface of the spherical region

r<a rel="nofollow" and; λ<a rel="nofollow" for any point within the surface

r and λ are complex beyond the surface

The wave dimension (λ) may be written as; λ = cT (where; T is time and; c is the light constant)

A spherical region having a constant surface radius (a) and space-time components (cT,x,y,z) may be defined as;

cT^2 + x^2 + y^2 + z^2 = a^2

Can a spherical region in 3D be represented using four dimensions?

Reference;

http://newstuff77.weebly.com 33 Cartesian Metrics