We introduce a “structure” of epic proportions – golden pyramid whose sacred geometry is “Fibonacci squared”. In terms of mathematical beauty, the golden pyramid will perhaps be found to be comparable to Pascal triangle.
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.
The possible variation of the fine-structure constant, a, has inspired many people to work on modifications and/or generalizations of the current "standard" theories in which the electromagnetic field is involved. Here we first point out the amazing similarity between Bekenstein's model, describing the variation of α by a varying charge, and the Hojman-Rosenbaum-Ryan-Shepley torsion potential model. This observation invites us to consider a geometric theory of gravity in which a varying α originates from another kind of dynamic quantity of spacetime, i.e., vector torsion. Since the vector torsion field is weak and also not strongly coupled with fermions it is difficult to detect it directly. The detection of a time-varying α could thus provide some promising evidence for the existence of torsion.