The cosmic spiral -- In radial coordinates
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The Cosmic Spiral In Radial Coordinates

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The Radii of the Cosmic Spiral

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The cosmic spiral would be the common form of the structure of many cosmic elements such as galaxies, ordering of orbitals in stars and atoms, etc.
Logically in these cases the number Pi would be basic, since it is a key number for the construction of spherical elements.
For its birth or construction, this spiral takes as its starting point the direction of the unit radius that is taken to build the formula of said spiral.
That is, taking a Cartesian coordinate axis, if we want to start building the spiral with birth in the x direction, then the natural radius of the spiral will be the direction of this x coordinate.
Well, the radius of each turn will increase in relation to Pi/2, and its simple formula would be Rn = R1. (Pi/2)^n,
Therefore the radius for each new turn will be obtained by multiplying the previous radius by Pi/2.
This type of spirals has the peculiarity that, measured the radii on the plane of the equator, the set of all of them form orbits around the central nucleus.