## 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.

## Quintessential Nature of the Fine-Structure Constant

Quintessential Nature of the Fine-Structure Constant  by  Michael Sherbon An introduction is given to the geometry and harmonics of the Golden Apex in the Great Pyramid, with the metaphysical and mathematical determination of the fine-structure constant of electromagnetic interactions. Newton’s gravitational constant is also presented in harmonic form and other fundamental physical constants are then found related to the quintessential geometry of the Golden Apex in the Great Pyramid.

## Fundamental Nature of the Fine-Structure Constant

Fundamental Nature of the Fine-Structure Constant by Michael A. Sherbon        Abstract: Arnold Sommerfeld introduced the fine-structure constant that determines the strength of the electromagnetic interaction. Following Sommerfeld, Wolfgang Pauli left several clues to calculating the fine-structure constant with his research on Johannes Kepler’s view of nature and Pythagorean geometry. The Laplace limit of Kepler’s equation in classical mechanics, the Bohr-Sommerfeld model of the hydrogen atom and Julian Schwinger’s research enable a calculation of the electron magnetic moment anomaly. Considerations of fundamental lengths such as the charge radius of the proton and mass ratios suggest some further foundational interpretations of quantum electrodynamics. International Journal of Physical Research, Vol. 2, No. 1 (2014).  Available at: http://www.sciencepubco.com/index.php/IJPR/article/view/1817  SSRN: 2380218 .                                                                                                                                       .

## Mathematical Constants of Natural Philosophy

Mathematical Constants of Natural Philosophy

– Michael A. Sherbon

Abstract: Plato’s theory of everything is an introduction to a Pythagorean natural philosophy that includes Egyptian sources. The Pythagorean Table and Pythagorean harmonics from the ancient geometry of the Cosmological Circle are related to symbolic associations of basic mathematical constants with the five elements of Plato’s allegorical cosmology: Archimedes constant, Euler’s number, the polygon circumscribing limit, the golden ratio, and Aristotle’s quintessence. Quintessence is representative of the whole, or the one in four, extraneously considered a separate element or fifth force. This relationship with four fundamental interactions or forces also involves the correlation of constants with the five Platonic solids: tetrahedron, hexahedron, octahedron, icosahedron, and dodecahedron. The values of several fundamental physical constants are also calculated, and a basic equation is given for a unified physical theory in the geometric universe of Plato’s natural philosophy.

SSRN Classics: Journal of Philosophical & Scientific Texts (July 21, 2010) SSRN: 1646568