While the proportion known as the Golden Mean has always existed in mathematics and in the physical universe, it is unknown exactly when it was first discovered and applied by mankind. It is reasonable to assume that it has perhaps been discovered and rediscovered throughout history, which explains why it goes under several names.

## Uses in architecture potentially date to the ancient Egyptians and Greeks

It appears that the Egyptians may have used both pi and phi in the design of the Great Pyramids. The Greeks are thought by some to have based the design of the Parthenon on this proportion, but this is subject to some conjecture.

Phidias (500 BC – 432 BC), a Greek sculptor and mathematician, studied phi and applied it to the design of sculptures for the Parthenon.

Plato (circa 428 BC – 347 BC), in his views on natural science and cosmology presented in his “Timaeus,” considered the golden section to be the most binding of all mathematical relationships and the key to the physics of the cosmos.

Euclid (365 BC – 300 BC), in “Elements,” referred to dividing a line at the 0.6180399… point as “dividing a line in the extreme and mean ratio.” This later gave rise to the use of the term mean in the golden mean. He also linked this number to the construction of a pentagram.

## The Fibonacci Series was discovered around 1200 AD

Leonardo Fibonacci, an Italian born in 1175 AD (2) discovered the unusual properties of the numerical series that now bears his name, but it’s not certain that he even realized its connection to phi and the Golden Mean. His most notable contribution to mathematics was a work known as Liber Abaci, which became a pivotal influence in adoption by the Europeans of the Arabic decimal system of counting over Roman numerals. (3)

## It was first called the “Divine Proportion” in the 1500’s

Leonardo Da Vinci provided illustrations for a dissertation published by Luca Pacioli in 1509 entitled “De Divina Proportione” (1), perhaps the earliest reference in literature to another of its names, the “Divine Proportion.” This book contains drawings made by Leonardo da Vinci of the five Platonic solids. It was probably da Vinci who first called it the “sectio aurea,” which is Latin for golden section.

The Renaissance artists used the Golden Mean extensively in their paintings and sculptures to achieve balance and beauty. Leonardo Da Vinci, for instance, used it to define all the fundamental proportions of his painting of “The Last Supper,” from the dimensions of the table at which Christ and the disciples sat to the proportions of the walls and windows in the background.

Johannes Kepler (1571-1630), discoverer of the elliptical nature of the orbits of the planets around the sun, also made mention of the “Divine Proportion,” saying this about it:

“Geometry has two great treasures: one is the theorem of Pythagoras; the other, the division of a line into extreme and mean ratio. The first we may compare to a measure of gold; the second we may name a precious jewel.”

## The term “Phi” was not used until the 1900’s

It wasn’t until the 1900’s that American mathematician Mark Barr used the Greek letter phi (Φ) to designate this proportion. By this time this ubiquitous proportion was known as the golden mean, golden section and golden ratio as well as the Divine proportion. Phi is the first letter of Phidias (1), who used the golden ratio in his sculptures, as well as the Greek equivalent to the letter “F,” the first letter of Fibonacci. Phi is also the 21st letter of the Greek alphabet, and 21 is one of numbers in the Fibonacci series. The character for phi also has some interesting theological implications.

## Recent appearances of Phi in math and physics

Phi continues to open new doors in our understanding of life and the universe. It appeared in Roger Penrose’s discovery in the 1970’s of “Penrose Tiles,” which first allowed surfaces to be tiled in five-fold symmetry. It appeared again in the 1980’s in quasi-crystals, a newly discovered form of matter.

## Phi as a door to understanding life

The description of this proportion as Golden and Divine is fitting perhaps because it is seen by many to open the door to a deeper understanding of beauty and spirituality in life. That’s an incredible role for a single number to play, but then again this one number has played an incredible role in human history and in the universe at large.

Source – The Divine Proportion : A Study in Mathematical Beauty by H. E. Huntley

(1) Page 25

(2) Page 157

(3) Page 158

^-^ says

The Golden Ratio is found in:

• Geometry

• Art

• Architecture

• Nature

• The human body

• And many other things

mayanj says

What do u mean by many others???

Gary Meisner says

Mathematics, design, the solar system, plants, animals, stock markets, beauty and cosmetic surgery to name a few. See http://www.goldennumber.net/site-map/ for the full list on this site.

Al lewis says

There’s more to the eye that these numbers represent. Numbers are a universal language. Their origin and placement in important designs and belief systems should be noticed. Can you connect the dots?

Jiahui says

nice work. it gave a lot help to my group when doing our project. Thanks for your resource. :):)

Waziri says

This is food for thought.

Abhipsa Mohanty says

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chasity Quarterman says

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Asynsis says

As a geometrical relationship of relationships (and taking a Platonic view), the Golden Ratio exists beyond time and space as it can be viewed as a logical system of information, like Godel’s incompleteness theorem. It needs no matter nor energy expression or substrate to exist independently as a Platonic archetype. This is the power of geometry – of which mathematics is just a code, like html is to this graphic webpage.

Explicit reference can be traced to Plato and Euclid but since it is often attributed to Pythagoras (and since Plato and Euclid are intellectual followers of Pythagoras), and the symbol of the Pythagoreans is the Pentagram or Five-pointed star that inspired Da Vinci’s Vitruvian man, which is Golden Ratio proportioned, it’s reasonable to assume he first popularised it.

Interestingly, he was a cross between John Cage, Spinoza, Newton and Julian Assange in fusing music, philosophy physics-mysticism and political resistance to tyranny, a true renaissance man before his time. It’s said that he went to Egypt and leant geometry from the Priest-Architects there, who as mathematicians and surveyors, used simple triangular geometry with ropes & pegs to remap the temple farm lands each year after the seasonal Nile floods. They perhaps would have shown him the Golden Ratio in the proportions of the Great Pyramid as well. So we could say it’s likely the Priest-Architects of ancient Egypt and Mesopotamia first codified the Golden Ratio in a cultural-economic and agricultural measurement response to the seasonal vagaries of the flooding Tigris, Euphrates and Nile.

The wealth generated from the exploitation of those lands allowed the construction of the magnificent temples and tombs we can still see there to this day,

All this measurement history however – is statics, it’s spatial.

For the temporal manifestation of the Golden Ratio and it’s role as the signature of the new Constructal design law of nature and culture, please refer to this seminar given late last year in Shanghai:

Cosmomimetic Design in Nature&Culture – Asynsis Principle-Constructal Seminar:

ShanghaiUniNantesEcoledeDesign http://wp.me/p1zCSP-1S via @ASYNSIS

http://asynsis.wordpress.com

http://constructal.org

http://www.forbes.com/sites/anthonykosner/2012/02/29/theres-a-new-law-in-physics-and-it-changes-everything/

Blissful Serenity says

The fingerprints of God!

jimmy junior says

I agree. This is obviously evidence of a God. The chance of this happening from a big bang (who’s the big banger) is 1 in infinity AND BEYOND (buzz lightyear joke). There must be some sort of conspiracy for this with BIG money behind it.

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Robert Jansen says

I find that one of the more interesting things about phi is the manner in which the division of adjacent pairs of the Fibonacci series converges to the limit. Pick any pair at random, and it will be either above or below the limit. The next pair, above or below, will be on the other side: the quotient of the adjacent pairs of the Fibonacci series will converge from alternate sides of the limit all the way to infinity.