## Physical Mathematics and the Fine-Structure Constant

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Abstract: Research into ancient physical structures, some having been known as the seven wonders of the ancient world, inspired new developments in the early history of mathematics. At the other end of this spectrum of inquiry the research is concerned with the minimum of observations from physical data as exemplified by Eddington’s Principle. Current discussions of the interplay between physics and mathematics revive some of this early history of mathematics and offer insight into the fine-structure constant. Arthur Eddington’s work leads to a new calculation of the inverse fine-structure constant giving the same approximate value as ancient geometry combined with the golden ratio structure of the hydrogen atom. The hyperbolic function suggested by Alfred Landé leads to another result, involving the Laplace limit of Kepler’s equation, with the same approximate value and related to the aforementioned results. The accuracy of these results are consistent with the standard reference. Relationships between the four fundamental coupling constants are also found.
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Inverse fine-structure constant is a root of: x4 – 136x3 – 136x2 – 818x + 1 = 0. This equation gives a value for x = 137.035 999 168 ….
CODATA (2014) Inverse alpha = 137.035 999 160 (33). The other root of the equation is approximately 1/818 and 818 = (136+1/3)6 = (4×136)+(2×137). OSF Preprints     Physical_Mathematics_and_the_Fine-Structure_Constant
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## Fine-Structure Constant from Golden Ratio Geometry

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After a brief review of the golden ratio in history and our previous exposition of the fine-structure constant and equations with the exponential function, the fine-structure constant is studied in the context of other research calculating the fine-structure constant from the golden ratio geometry of the hydrogen atom. This research is extended and the fine-structure constant is then calculated in powers of the golden ratio to an accuracy consistent with the most recent publications. The mathematical constants associated with the golden ratio are also involved in both the calculation of the fine-structure constant and the proton-electron mass ratio. These constants are included in symbolic geometry of historical relevance in the science of the ancients.

$\alpha^{-1}\simeq\frac{360}{\phi^{2}}-\frac{2}{\phi^{3}}+\frac{\mathit{A^{2}}}{K\phi^{4}}-\frac{\mathit{A^{\mathrm{3}}}}{K^{2}\phi^{5}}+\frac{A^{4}}{K^{3}\phi^{7}}\simeq137.035\,999\,168&space;.$

$A=e^{\pi}-7\pi-1$

α is the fine-structure constant, φ is the Golden Ratio, A is the Golden Apex of the Great Pyramid and K is the polygon circumscribing constant. 2016 CODATA: 137.035 999 160 (33).

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## Fundamental Physics and the Fine-Structure Constant

From the exponential function of Euler’s equation to the geometry of a fundamental form, a calculation of the fine-structure constant and its relationship to the proton-electron mass ratio is given. Equations are found for the fundamental constants of the four forces of nature: electromagnetism, the weak force, the strong force and the force of gravitation. Symmetry principles are then associated with traditional physical measures.

## Michael Sherbon’s Review > The Giza Template: Temple Graal Earth Measure by Edward G Nightingale, Laird Scranton (Afterword)

What a surprise! This work might be a milestone achievement in the history of science. Edward G. Nightingale may not fully realize the breakthrough discovery that he has made. While it seems as though it aims to support the theories of Robert Bauval et al, it has a much larger application. He begins with Plato’s Lambda and calculates several different types of cubits. And this shows that the Lambda did not originate with Plato or the Pythagoreans and was probably part of the initiate knowledge they brought back with them to Greece from their study in Egypt.

Jocelyn Godwin, in Harmonies of Heaven and Earth, states “Albert von Thimus (1806-1878), a polymathic researcher into ancient harmonic theory, …” called Plato’s Lambda (from Iamblichus) the Lambdoma. “Thimus developed the Lambdoma into a square diagram, which he called the ‘Pythagorean Table’ … Both von Thimus and his spiritual heir, Hans Kayser, believed that this was the fundamental diagram of the lost ancient science of Harmonics, hinted at by Plato … as the culmination of all learning, but never revealed publicly. Others say that von Thimus was mistakenly projecting on the the ancient Pythagoreans his own discovery of a scheme typical of early nineteenth-century mathematical theory.” (Rene Guenon, The Symbolism of the Cross)

From the Pythagorean Table or Lambdoma described by Thomas Hightower in The Musical Octave … “Mathematicians and scientists have studied the Lambdoma since its discovery. It is said to hold the many esoteric secrets of the relationship between matter and spirit, including being a numerical representation of the World Soul…. In the 1920s Hans Kayser, a German scientist, developed a theory of world harmonics based upon the Lambdoma. He found that the principles of harmonious structure in nature and the fundamentals of harmonics were essentially the same….

Kayser believed that this knowledge of harmonics had become lost and had created a major schism between science and the spirit. He hoped that a true understanding of this relationship would create a bridge between the matter and soul…. According to Kayser, the whole number ratios of musical harmonics corresponds to an underlying framework existing in chemistry, physics, crystallography, astronomy, architecture, spectroanalysis, botany and the study of other natural sciences. The relationship expressed in the periodic table of elements, an understanding of the formation of matter, resembles the overtone structure in music….”

What Edward has done is to demonstrate von Thimus to be correct, and has opened the way to further discovery on the Great Pyramid itself. Laird Scranton reminds us of the Hermetic axiom, “As above, so below. As within, so without.” The Great Pyramid is as Manly P. Hall stated a scale model of both the microcosm and the macrocosm. The precession of the equinoxes for earth is an analog for the precession of the electron in hydrogen. Herodotus reported that the Great Pyramid was a “wonder of physics.”

Bruce Cathie rediscovered some of this harmonic theory from the ancient world grid artifacts. William Conner, in Harmonic Mathematics, developed a revised Pythagorean Table and showed some of the basic dimensions of the Great Pyramid encoded these harmonics. Robert K.G. Temple, in Egyptian Dawn, has also made a significant contribution to the plan on the Giza Plateau, describing the importance of the Pythagorean Comma and the Golden Angle of Resurrection. Goodreads