Working the sphere packing issue with Fibonacci

Evidently the physics community has not bought the idea the Fibonacci makes for good sphere packing, so I am working on it. Still at the fumbling around stage, except to note that the slightly different sizes in the two phase bubble ensure a radial axis of symmetry and a curvature in free space. I am looking the the three sphere model. The main thing is the three sphere generates a division. And that leads me to group theory, the place I wanted to avoid.

I think I will discover that the actual rate, the Fibonacci, results because it is the most irrational number; hence it is simply a result of use humans applying an accurate number line to the measurements of physics. This sounds vague, mainly because I am once again a bit above my head.

But, here is the plan.  The three space makes for a quotient space, valid within the curvature determined by difference in sphere size, leading to a minimum sample rate which must be most irrational number, as a sample rate. That is the sample rate (temperature, or measure of disorder) cannot measure itself, by definition. Hence the Fibonacci rate will fall out by definition of us humans maximally counting the things that three different size bubbles can do. And, once again, the hyperbolics fall out as the natural power series expansion.

 Before I go too far, some recognition of work by others:

Measurement of areas on a sphere using Fibonacci and latitude-longitude latticesThe area of a spherical region can be easily measured by considering which sampling points of a lattice are located inside or outside the region. This point-counting technique is frequently used for measuring the Earth coverage of satellite constellations, employing a latitude-longitude lattice. This paper analyzes the numerical errors of such measurements, and shows that they could be greatly reduced if the Fibonacci lattice were used instead.

And the Phi Bar:

Phi relationships in a color spectrum produce rich, appealing color combinations

Michael Semprevivo has introduced a concept called the PhiBar, which applies phi relationships to frequencies, or wavelengths, in the spectrum of visible colors in light.  Colors in the spectrum that are related by distances based on phi or the golden section produce very rich and visually appealing combinations.

Perfect light transmission in Fibonacci arrays of dielectric multilayers

Localization of light waves in Fibonacci dielectric multilayersWe have measured the optical transmission of quasiperiodic dielectric multilayer stacks of SiO2 (A) and TiO2 (b) thin films which are ordered according to a Fibonacci sequence Sj+1={Sj-1}, with S0={B} and S1={A} up to the sequence S9 which consists of 55 layers. We observe a scaling of the transmission coefficient with increasing Fibonacci sequences at quarter-wavelength optical thicknesses. This behavior is in good agreement with theory and can be considered as experimental evidence for the localization of the light waves. The persistence of strong suppression of the transmission (gaps) in the presence of variations in the refractive indices among the layers is surprising.

Unfortunately, here I go, and this is a three week project, using the fake variable time.