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### Re: Keplers Cross

From Mysterium Cosmographicum:

I don't work with lead, but straw can become gold too.  Takes a good spinning wheel.

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### Re: Keplers Cross

13.4/1836.15 = 0.00729787871361
and the way done (The Royal Orb Way) it is dimensionless.

The band around the orb illustrates the electron of course!

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### Re: Keplers Cross

Well, I know that Feynman's number was, as he said, "close to 0.08542455." And he also said "My physicist friends won't recognize this number, because they like to remember it as the inverse of its square: about 137.03597 with an uncertainty of about 2 in the last decimal place."

So maybe that is a hint too.  I wish others luck with this - will watch from a safe distance - maybe a few parsecs from here.  :)

**

Actually I will provide another answer though.

If we flip the work on my previous post and divide 1836.15 by 13.4, we get

137.02611940298507

That is very close.

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### Re: Keplers Cross

if done accurately the Royal Orb Way is off by $\frac{\alpha_{C}-\alpha_{Royal}}{\alpha_{C}}=0.0161\%$ from CODATA. I would trust the Queen, so CODATA is off by 0.0161% .

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### Re: Keplers Cross

we can use this method also to calculate such things as very precise ionization energy without having to relay on obscure methods. We should trust Kepler

"Sommerfeld, in 1916, solved the relativistic Kepler problem and using the old quantum theory, as it later christened, accounted precisely for the splitting."

Old quantum is good, ancient quantum even better. And the Modern Fashion?

However to get excellent fit to the experimental observations do not forget the Lamb shift adjustment (tilting of the cross)

For example for copper (29) I get 11577 electron volts in ionization energy before Lamb shift when using the Kepler cross in relativistic calculations. This is a few electron volts off experimental values. After Lamb shift adjustment I get a value very close to the experimental value of 11568

Tips 10: Do not forget to look further into the packing of the Platonic solids.

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### Re: Keplers Cross

On the Platonic solids, for the most efficient packing, we might convert 0.08542455 in a percent and see if each one is 8.542455% smaller than the one preceding (enveloping) it does that work?

See the schematic I posted earlier.

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### Re: Keplers Cross

There is a direct connection between low discrepancy sequences used in Monte Carlo sampling in finance, and sphere packing. The orange pyramid is the most dense regular packing, in higher dimensions it's still an open problem.

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### Re: Keplers Cross

Nice paper:

Dense Packings of Polyhedra: Platonic and Archimedean Solids

S. TorquatoY. Jiao (2009) See links to additional work by the authors also.

Abstract:
We formulate the problem of generating dense packings of nonoverlapping, non-tiling polyhedra within an adaptive fundamental cell subject to periodic boundary conditions as an optimization problem, which we call the Adaptive Shrinking Cell (ASC) scheme. This novel optimization problem is solved here (using a variety of multi-particle initial configurations) to find the dense packings of each of the Platonic solids in three-dimensional Euclidean space R3 , except for the cube, which is the only Platonic solid that tiles space. We find the densest known packings of tetrahedra, icosahedra, dodecahedra, and octahedra with densities 0.823, 0.836, 0.904, and 0.947, respectively. It is noteworthy that the densest tetrahedral packing possesses no long-range order. Unlike the densest tetrahedral packing, which must not be a Bravais lattice packing, the densest packings of the other non-tiling Platonic solids that we obtain are their previously known optimal (Bravais) lattice packings. We also derive a simple upper bound on the maximal density of packings of congruent nonspherical particles, and apply it to Platonic solids, Archimedean solids, superballs and ellipsoids. Our simulation results, rigorous upper bounds, and other theoretical arguments lead us to the conjecture that the densest packings of Platonic and Archimedean solids with central symmetry are given by their corresponding densest lattice packings. In addition, we conjecture that the optimal packing of any convex, congruent polyhedron without central symmetry generally is not a lattice packing.

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### Re: Keplers Cross

http://www.datasimfinancial.com
http://www.datasim.nl

Approach your problem from the right end and begin with the answers. Then one day, perhaps you will find the final question..
R. van Gulik

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### Re: Keplers Cross

what is that? a scan of your eye or brain? or bee hive hexagons? Or just smile packed smily faces? are they lamb shifted?

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### Re: Keplers Cross

It's diffraction grating lots of packing.

http://www.datasimfinancial.com
http://www.datasim.nl

Approach your problem from the right end and begin with the answers. Then one day, perhaps you will find the final question..
R. van Gulik

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### Re: Keplers Cross

okay then, Tips 7: the Music of the spheres indicated spheres and certain harmonic formations of spheres.
Only indivisible spheres are immortal (the atoms of Democritus and Leuppikus).
Kepler would have gathered the Divine 7 by sphere packing (Kepler conjecture).
And closed the gates to the cross with 2 Gate keepers, the Guardians of the Cross.

And yes the average of the cross arms is irrational! And is a very important ratio in terms of Magic Numbers hidden in Nature.

Maybe relevant wrt HEXAGON packing theorems.
https://www.math.utk.edu/~kens/
http://www.datasimfinancial.com
http://www.datasim.nl

Approach your problem from the right end and begin with the answers. Then one day, perhaps you will find the final question..
R. van Gulik

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### Re: Keplers Cross

okay then, Tips 7: the Music of the spheres indicated spheres and certain harmonic formations of spheres.
Only indivisible spheres are immortal (the atoms of Democritus and Leuppikus).
Kepler would have gathered the Divine 7 by sphere packing (Kepler conjecture).
And closed the gates to the cross with 2 Gate keepers, the Guardians of the Cross.

And yes the average of the cross arms is irrational! And is a very important ratio in terms of Magic Numbers hidden in Nature.

Maybe relevant wrt HEXAGON packing theorems.
https://www.math.utk.edu/~kens/
don't forget the circle packing show

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### Re: Keplers Cross

Here is a presentation from MIT:

Sphere Packing IAP Math Lecture Series - Henry Cohn Jan 2015

It starts from the basics, but goes quite deep.  By the end you are looking at packing in high dimensions and also some work on "remarkable packings" like R8:E8Root lattice and R24:E24 Leech lattice.

The presentation concludes with a few citations of recent work, including Vance (2011) on quaternion algebras and Venkatesh (2012) on cyclotomic fields.

So it may be of interest to those who are packing our crystalline skulls with thoughts of spheres.

Take care if the outer structure is fragile!

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### Re: Keplers Cross

Tips 11: Newton knew more deep physics than he told the public. Study his alchemical manuscripts in detail and try to understand why he was the Warden of the Royal Mint.

His transmutation formula is Glorious!