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

  1. #1 Can a spherical region in 3D be represented using four dimensions? 
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    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


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  3. #2  
    exchemist
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    Quote Originally Posted by RichardK View Post
    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?

    Word salad?

    Ah you seem to be Richard 777, the drive-by spammer, from earlier this year, on another forum.


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  4. #3  
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    Quote Originally Posted by RichardK View Post
    regions within and beyond the surface are undefined.
    Why do you think that? They are defined just fine.
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