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Why is (1.61803399) considered the golden ratio?
The golden ratio is special. That's why it is also known as the divine proportion, golden mean, or golden section. It’s a powerful number mathematically. For example, in the universe of all ratios, it is the only one where the ratio of the large part to the small is the same as the ratio of the large part to the sum of the large and small. This fractal property plays into physics in many ways.
The golden ratio, in its integer form is the Fibonacci sequence, where the ratio of each sequential pair of such numbers approximates the golden ratio and terminates at its limit at exactly the golden ratio. It holds a record. Of all series, it approaches its limit faster than any other.
It holds a second record. In it’s continued fraction form, it approaches its limit slower than any other, due to the fact that it uses only 1s. And this limit plays deeply into physics. The KAM theorem shows that tori in nature are more probable when the ratio of inner to outer diameters is irrational. A follow up work showed that the probability of finding tori in nature, scales with the rank of irrationality of the aforementioned torus dimensions. Mathematicians prove the rank of irrationality of a number based on how slowly its continued fraction form approaches convergence. Accordingly, tori in nature with golden ratio based dimensions survive under perturbation more than any other, i.e., the probability or frequency of tori in nature ranks with how close they are described by the golden ratio. Note that an extruded torus is a vortex. And vortices exist in gravitational physics, quantum physics, and any physics related to fluid dynamic equations.
The shortest algorithm to distribute points on a sphere uses the golden ratio exactly because it is the most irrational of numbers.
And this too is a physical concept with respect to repelling charges in circular or spherical boundaries. There is much more. The golden ratio is the basis of all 300 of the known 3D quasicrystals discovered so far. This is a new state of matter discovered only in 1984, which won Dan Shechtman The Nobel Prize in Chemistry 2011.
You can access our paper 'Quantum Walk on a Spin Network and the Golden Ratio as the Fundamental Constant of Nature' here, which was published by Minkowski Institute Press. You can access and order the Minkowski publication, which is dedicated to the 100th anniversary of the publication of General Relativity, here: General Relativity 1916 - 2016. Selected peer-reviewed papers presented at the Fourth International Conference on the Nature and Ontology of Spacetime.
Our group, Quantum Gravity Research is one of the largest groups in the world working on unification physics. The basis of our formalism is quasicrystal mathematics. To learn more through our many presentations, including our "Quantum Chat" and "Raw Physics" videos, you can access on our Quantum Gravity Research Youtube Channel.