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Top Pages Related to: Polar Coordinates

  • => ULTIMATE SYMMETRY - IV.2 Ultimate Symmetry of Constant Entities
  • ... , first into the hyper symmetry of the spiritual world, and then into the super symmetry by breaking one spatial dimension into two arrows of time as we discussed in Chapters II and III. In polar coordinates, for example, if space is described by the spherical symmetry , which is equivalen ...


  • => ULTIMATE SYMMETRY - I.2.1 Fractals and Divergent Series
  • ... is impossible in the actual physical world.   However, Lorentz transformations are equivalent to a rotation in the imaginary plane, since: , while , and we have seen above that in the polar coordinates, where a unit circle is defined by: , we could split this circle into two conjugat ...


  • => DUALITY OF TIME - 7.2  The Hidden Symmetry
  • ... , by noting that the resulting time directions are split-imaginary, or hyperbolic, numbers. Therefore, the two opposite time directions are two conjugate complex numbers, thus: , or in the polar coordinates, each point in the resulting positive space-time can be expressed in the form: , w ...


  • => DUALITY OF TIME - 7.3.1  The Problem of Infinity
  • ... ctual physical world. However, as we have seen in chapter V, Lorentz transformations are equivalent to a rotation in the imaginary plane, since: , while , and we have seen above that in the polar coordinates, where a unit circle is defined by: , we could split this circle into two conjugat ...


  • => DUALITY OF TIME - 3.3.4  The FLRW Metric
  • ... onal space of uniform curvature, that is, elliptical space, Euclidean space, or hyperbolic space. It is normally written as a function of three spatial coordinates. In reduced-circumference polar coordinates the spatial metric has the form: (3.13) Here, , is a constant representing the cur ...



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    • ... Islamic Cosmology =>:

    • ... Space Transcendence Read this short concise exploration of the Duality of Time Postulate: DoT: The Duality of Time Postulate and Its Consequences on General Relativity and Quantum Mechanics ...


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    • ... Space Transcendence Read this short concise exploration of the Duality of Time Postulate: DoT: The Duality of Time Postulate and Its Consequences on General Relativity and Quantum Mechanics ...


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    • ... Time Postulate: DoT: The Duality of Time Postulate and Its Consequences on General Relativity and Quantum Mechanics ...


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    • ... hich may be taken to have units of length-2, and is like the Schwarzschild radius, as well as the other parameters, as we have seen in section 3.3 above.     Read Other Books: The SINGLE MONAD MODEL of the Cosmos: Ibn Arabi's View of Time and Creation The Duality of Time Theory: ...


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    • ... ;   Read Other Books: The Single Monad Model of the Cosmos: Ibn Arabi's View of Time and Creation The Duality of Time Theory: Complex-Time Geometry and Perpertual Creation of Space The ULTIMATE SYMMETRY : Fractal Complex-Time and Quantum Gravity The Chest of Time: Particle-Wave Duality ...


    • ... Cosmology =>:

    • ... eity and isotropy; Einstein’s field equations are only needed to derive the scale factor of the Universe as a function of time. This model is also called the Standard Model of modern cosmology, which is also associated with the further developed Lambda-CDM model, as described in sec ...


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    • ... scendence Read this short concise exploration of the Duality of TIME Postulate: DoT: The Duality of TIME Postulate and Its Consequences on General Relativity and Quantum Mechanics ...


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    • ... 931. The problem was investigated further by Howard Robertson (1903-1961) and Arthur Walker (1909-2001), who rigorously proved, in 1935, that the now called FLRW metric is the only one on a space-time that is spatially homogeneous and isotropic, but this is a geometric result that is not t ...


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    • ... Space Transcendence Read this short concise exploration of the Duality of Time Postulate: DoT: The Duality of Time Postulate and Its Consequences on General Relativity and Quantum Mechanics ...


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    • ... Space Transcendence Read this short concise exploration of the Duality of Time Postulate: DoT: The Duality of Time Postulate and Its Consequences on General Relativity and Quantum Mechanics ...


    • ... General Relativity =>:

    • ... e this Book 3.3.4  The FLRW Metric In 1922, Alexander Friedmann (1888-1925) published a paper in which he describes a homogeneous, isotropic expanding or contracting Universe, based on GENERAL RELATIVITY . Although his paper was refereed by Einstein and published in the prestigious phy ...


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    • ... me Confinement to Space Transcendence Read this short concise exploration of the Duality of Time Postulate: DoT: The Duality of Time Postulate and Its Consequences on General Relativity and QUANTUM MECHANICS ...


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    • ... Space Transcendence Read this short concise exploration of the Duality of Time Postulate: DoT: The Duality of Time Postulate and Its Consequences on General Relativity and Quantum Mechanics ...


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    • ... Space Transcendence Read this short concise exploration of the Duality of Time Postulate: DoT: The Duality of Time Postulate and Its Consequences on General Relativity and Quantum Mechanics ...


    • ... Symmetry =>:

    • ... Read Other Books: The Single Monad Model of the Cosmos: Ibn Arabi's View of Time and Creation The Duality of Time Theory: Complex-Time Geometry and Perpertual Creation of Space The Ultimate SYMMETRY : Fractal Complex-Time and Quantum Gravity The Chest of Time: Particle-Wave Duality: from Ti ...


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    • ... Space Transcendence Read this short concise exploration of the Duality of Time Postulate: DoT: The Duality of Time Postulate and Its Consequences on General Relativity and Quantum Mechanics ...


    Welcome to the Single Monad Model of the Cosmos and Duality of Time Theory
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    I have no doubt that this is the most significant discovery in the history of mathematics, physics and philosophy, ever!

    By revealing the mystery of the connection between discreteness and contintuity, this novel understanding of the complex (time-time) geometry, will cause a paradigm shift in our knowledge of the fundamental nature of the cosmos and its corporeal and incorporeal structures.

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