Further to early humans preferred the Golden Ratio (1.618) too?: Repeated use of the numbers 2, Pi and Phi and the relationship between them could not have been chance.

I, O’Leary for News, wish to thank bornagain for consistently helpful notes in the comments over the years, and to draw attention to his notes on the Golden Ratio in particular:

The golden ratio is found throughout nature and has often been referred to as ‘the fingerprint of God’ (vid ):

From the shape of some galaxies to quantum mechanics, the golden ratio is found throughout nature.

Do We Live in a “Golden Ratio” Universe? (*Evolution News & Views* December 2, 2014)

*The curl of an elephant tusk

*The shape of a kudu’s horn

*Hurricane spirals

*The distribution of planets in the solar system

*A biological species constant, T

*The spiral structure of the cochlea ear-bone in a fossil hominin

*The logarithmic spirals of galaxies

*The structure of DNA

*The growth of many plants (phyllotaxis)

*The Periodic Table of the Elements

*Spiral shells of certain mollusks, like snails

*Spiral shells of living and extinct ammonites

*Stress patterns in nanomaterials

*The stability of atomic nuclides

*The topology of space-time

What is sculpting the Milky Way into its beautiful spiral shape? In the following article it is claimed that ‘the topology of space-time’ itself is based on the golden ratio and, as such, could be very instrumental in explaining why the Milky Way forms such a beautiful spiral shape (2014):

We suggest that there is a strong case that this so-called ‘Golden Ratio’ (1.61803…) can be related not only to aspects of mathematics but also to physics, chemistry, biology and the topology of space-time…

As well, the golden ratio is found on the quantum scale:

Golden ratio discovered in quantum world: Hidden symmetry observed for the first time in solid state matter (January 7, 2010)

Excerpt: For these interactions we found a series (scale) of resonant notes: The first two notes show a perfect relationship with each other. Their frequencies (pitch) are in the ratio of 1.618…, which is the golden ratio famous from art and architecture.” Radu Coldea is convinced that this is no coincidence. “It reflects a beautiful property of the quantum system — a hidden symmetry. Actually quite a special one called E8 by mathematicians, and this is its first observation in a material,” he explains.

‘Fibonacci quasiparticle’ could form basis of future quantum computers (Dec. 15, 2014) Excerpt: “The Fibonacci anyon is a non-Abelian anyon whose quantum dimension is the golden ratio (1.617…), and is the simplest anyon capable of performing universal quantum computation,” Vaezi explained. “Using the fusion rule of Fibonacci anyons, it can be shown that the degeneracy of the ground state in the presence of n well-separated Fibonacci anyons on a sphere is the nth number in the Fibonacci sequence.”

Notes: In physics, an anyon is a type of quasiparticle that occurs only in two-dimensional systems, with properties much less restricted than fermions and bosons… the Nth Number is some arbitrary positive integer in a sequence.

DNA also has the beauty of the golden ratio embedded within it:

DNA spiral as a Golden Section

Excerpt: The DNA molecule, the program for all life, is based on the golden section. It measures 34 angstroms long by 21 angstroms wide for each full cycle of its double helix spiral. 34 and 21, of course, are numbers in the Fibonacci series and their ratio, 1.6190476 closely approximates phi, 1.6180339.

DNA in the cell appears as a double-stranded helix referred to as B-DNA.This form of DNA has a two groove in its spirals, with a ratio of phi in the proportion of the major groove to the minor groove, or roughly 21 angstroms to 13 angstroms.

… a cross-sectional view from the top of the DNA double helix forms a decagon:

A decagon is in essence two pentagons, with one rotated by 36 degrees from the other, so each spiral of the double helix must trace out the shape of a pentagon.

The ratio of the diagonal of a pentagon to its side is Phi to 1. So, no matter which way you look at it, even in its smallest element, DNA, and life, is constructed using phi and the golden section!

Cross section of DNA compared to the Rose window at York Minster (the largest Gothic cathedral in northern Europe)

The golden ratio is not only beautiful to look at but it even sounds beautiful when put to music.

One doesn’t hear much about this sort of thing outside of compulsory math classes. Probably because our culture is much more attuned to forgettable books on why everything is a cosmic accident

Reader-contributors like BA77 make a great deal of difference to a shoestring operation like ours. So again, thanks.

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