# Is there a divine proportion in nature?

Is there a divine proportion or ratio in nature that, somehow, we intuitively recognize as being right or pleasing?

This idea is not new but actually can be traced back to antiquity. The ancient Greeks believed it was discovered by Pythagoras and the 'father of Geometry' Euclid - a Greek mathematician is attributed with the first known recording of the ratio in writing.

Renaissance artists have applied this divine relationship in their works as have architects and all manner of designers including web designers for page layouts.

If you have a business card in your pocket take it out now and check the rectangle. Measure the long side and the short side and you will find a standard card conforms very closely to this ratio.

We see rectangles everywhere.

Some studies suggest most people prefer objects which conform to the Golden ratio but computer screen resolutions do not seem to conform to this divine ratio though we spend so much time staring at them and the trend is for them to be getting further away (not closer) to the ratio as computer users prefer bigger screens above 1024X768 (whose ratio is 1.3333...) See http://www.w3schools.com/browsers/browsers_display.asp

However, on the other hand, layouts and spaces on the webpages displayed on screens may (more often than not?) display the proportions as web designers use this ratio for object positioning on pages.

The rectangle conforming to the Golden ratio has been used extensively by artists, designers and architects.

So what is it exactly?

It is a number like Pi (which you might remember from your days working out the area of a circle).

Known as Phi (which is a letter in the Greek alphabet), the number is approximately 1.6180339887... and when you divide this number into one (its inverse) you get the number less one. That is 1.6180339887...-1 or 0.6180339887...

That is in itself a weird coincidence and the following number sequence 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987 ...named after Leonardo Fibonacci also holds a surprising and relevant outcome.

The sequence is built by adding the number that is the sum of the two preceding it. In other words, any number in the sequence is the sum of the two before.

As you move further along this sequence the previous number divided by the one that comes after it will get closer and closer to the divine ratio (1.6180339887...)

Fibonacci was an Italian mathematician of the 13th century and famous for spreading the word about using Arabic numerals instead of Roman numerals in his *Liber Abaci* (1202) and the Fibonacci sequence named after him is often mentioned with the Golden ratio.

Lastly, if you divide the width of the right column on this hub into the width of the column you are reading (on the left) what do you get?

It was pretty close (1.712) when I tried it.

And how about this...how close to 1.6180338667... is the ratio between the hubs you have written and your followers? Come On!

Mine...2.5135...I better get a wriggle on!

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## Comments 14 comments

Wow, this is way too deep for me, and I would never dare go and tackle, 'coz its mathematics and I think it didn't like me from the very start. I almost failed in college. Lol!

But tackling mathematical equations as part of nature is awesome, jaw-dropping, and a "How-I-wish-I-could-too" part of me. Lol!

Ancient and modern metaphysicians have attempted to generally link the macro and micro structure of the cosmological overview of the universe for millenia. The majority of attempts have followed the category of philosophy linked with reality, attempts mostly following the mathematical genre. The problem with both efforts have been the philosophical renderings lacking the solid boundaries of physical realities , while the physical attempts lacking the intuitional language that describes philosophy. The bridge between these two forms have unfortunately been widely separated in application. The problem has always been presented as linking the galactic scales of the universe to the atomic scales of matter. This dilemna can now be resolved ( 2012 ) due to studies of the ultimate root of matter ( black holes ) and the philosophical idea of the creation of matter ( Big Bang-Genesis ) linked by mathematics. This idea is defined by the ancient mantra of philosophers as: " As Above , So Below " , where the " Above " represents the macro-universe , while " Below " insinuating the micro-universe.

This dilemna has been resolved due to an article published in June,2 , 2011 , called , " A Link Between Black Holes and the Golden Ratio " , by J.A. Nieto:

arXiv:1106.1600v1[physics.gen-ph]

www.citeulike.org/group/10219/article/9395579

....the abstact of the article states:

" We consider a variational formalism to describe a black hole solution in higher dimensions. Our procedure clarifies the arbitrariness of the radius parameter and in particular, the meaning of the event horizon of a black hole. Moreover, our formalism enables us to find a surprising link between black holes and the golden ratio. "

...the article goes on to conclude that:

" ...rotating black holes make a phase transition when the ratio of the square of its mass to the square of its angular momentum is equal to the golden ratio."

The mathematics of Nieto's article is very complex , involving Hamiltonian and Lagrangian mathematics. However the result of his conclusion, the importance of the golden ratio is what is the key to the micro-macro structure of the universe. Since the gravitational constant , Gn , is the ultimate defining force of the structure of black holes , the constants that make up Gn has a micro black hole in its structure ..the Planck mass (Mp).

Gn = h * c / 2 / Pi / ( Mp^2 ) = 6.67384 * 10^-11 m^3 /kg/s^2 ............( exact 2012 NIST )

...where:

h = Plancks constant = 6.62606957 * 10^-34 J ....... ( exact 2012 NIST )

c = speed of light = 299792458 m/s ....... ( exact 2012 NIST )

Mp = Planck mass = 2.176509252 * 10^-8 kg .......( exact 2012 NIST )

Pi = 3.141592654

....this mass, Mp , is the secret to uniting the macro and micro structure of the universe. In the macro-universe the defining characteristic of the expansion of the universe since the Big Bang, is the famous Hubble constant ( Hb ) since defined as of 2012 as ...72 kilometers per second per megaparsec. To define the Hubble constant to the micro black hole , Mp , one has the formula:

( Hb ^ 2 ) / 4 / Pi / Gn / ( 10^13 ) = 1/ phi = .6180339875 ......Hb = 71.9944482 km/s/megaparsec

This formula defines the macro-universe. What about the micro-universe? The micro-universe is defined by the substance that makes up 98% of the mass of the universe , the Hydrogen atom, defined on the periodic table as 1.00794 atomic mass units or 1.00794 a.m.u.. This mass can be transformed into kilograms ,kg , by the Avogadro constant: Av = 6.02214129 * 10^23 moles...( exact 2012 NIST )

Ho = mass of Hydrogen atom = 1.00793995275 / Av / 10^ 3 = 1.673723522 * 10^-27 kg

.....the Hydrogen mass is made up of one proton and one electron. One of the great mysteries in Nature is the problem of the mass defect of the Hydrogen atom, which is accounting for the lost mass that occurs when one accounts for the individual masses of the proton and electron with the actual mass of the Hydrogen atom. This is called the mass defect problem , since resolved from the 1920s forward by various complicated formulas ( Hamiltonian and Lagrangian mathematics ) derived from various sources , Shroedinger, Pauli , Bohr , Einstein , Rutherford , etc. , using extremely complex mathematics to account for this lost mass involing the constituents of the Hydrogen atom , one proton and one electron. This problem of " mass defect " can be resolved by one simple sentence:

" One energy unit divided by the difference between the Hydrogen atom , Ho , and the proton , Mpr , masses equals phi , the golden ratio. "

....where

Ho = hydrogen mass = 1.673723522 * 10^-27 kg

Mpr = proton mass = 1.672621776 * 10^-27 kg .... ( exact 2012 NIST )

.....this simple sentence explains everything about the universe since the cosmos is made up of 98% Hydrogen beginning from the Big-Bang ( Genesis ) . One energy unit is derived from the Einsteinian conversion formula used in modern physics:

ev * ( 10^6 ) / c^2 = 1.782661845 * 10^-30 kg

....where:

ev = elementary charge = 1.602176565 * 10^-19 volts ....... ( exact 2012 NIST )

...the Genesis formula as follows:

ev * ( 10^6 ) / ( c^2 ) / ( Ho - Mpr ) = phi = 1.6180339875 = the golden ratio

....the macro and micro universe can now be equivicated:

4 * Pi * Gn * ( 10^13 ) / ( Hb^2 ) = phi = ev * ( 10^6 ) / ( c^2 ) / ( Ho - Mpr ) = the golden ratio

As Above So Below

....this form also solves the mystery of the link between Coulombs law and the Gravitational law:

k * ( ev^2 ) / Gn / ( Mp^2 ) = the fine-structure constant = aem = 1/137.0359991 ....( exact 2012 NIST )

....the fine-structure constant , aem , can now be shown as following the metaphysical statement , " As Above , So Below "

( Hb^2 ) * ( Ho - Mpr ) * ( phi^2 ) * ( Mp^2 ) / 4 / ( ev^3 ) / Pi / ( 10^12 ) = 137.0359991

....where:

Hb = hubble constant = 71.99444862 km/s/megaparsec

k = Coulombs constant = 8987551787 = c^2 / 10^7 ....( exact 2012 NIST )

Ho = Hydrogen mass = 1.673723522 * 10^-27 kg

Mp = Planck mass = 2.176509252 * 10^ -8 kg ....( exact 2012 NIST )

Mpr = proton mass = 1.672621776 * 10^-27 kg ....( exact 2012 NIST )

ev = electron charge = 1.602176565 * 10^-19 v ....( exact 2012 NIST )

J. Iuliano 1-22-2012

If you look this picture , see center, this hard =(

Very well put for such a complicated subject. Did you select the YouTube video to use on this hub? I frequently use the golden rectangle proportions in my work, and often, when a painting just isn't working, I can use it for a reference to create something that will make the piece come together. Thanks!

Pen

I don't know if it's divine, but those numbers seems to exist all around us. Fibonacci numbers are even applied by stocks and currency traders.

Mathematical relationships do indeed exist in nature but that's just a statistical reality. There can be no reason to attach some divine meaning to it. The numbers would still have the same relationship and would have no choice because that's the way numbers work.

My favourite number is the square root of 2 which is infinite... as is Pi.

16 to 9 is the ratio of width to height of modern televisions and movie theater screens. That ciphers out to 1.7777777777777777777777777777778 according to my Windows calculator.

I always marvel at hubbers who have a huge followers to hubs ratio. Mine is barely above 1. No one really likes me.

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