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

1. 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 and; λ<a 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  2.

3. Originally Posted by RichardK 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
What wave and what is meant by a wave dimension?

Ah you seem to be Richard 777, the drive-by spammer, from earlier this year, on another forum.  4. Originally Posted by RichardK regions within and beyond the surface are undefined.
Why do you think that? They are defined just fine.  Bookmarks
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