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# History

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 date to the ancient Egyptians and Greeks

Euclid (365BC - 300BC), 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.

The Egytians used both pi and phi in the design of the Great Pyramids. The Greeks, who called it the Golden Section, based the entire design of the Parthenon on this proportion. It was also used by Phidias, a famous Greek Sculptor. (1)

### 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

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 to designate this 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.  By this time this ubiquitous proportion was known as the golden mean, golden section and golden ratio as well as the Divine proportion.

### 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.

(1) Page 25
(2) Page 157
(3) Page 158

Phi - The Golden Number
A source to some of Net's "phi-nest" information on the
Golden Section / Mean / Proportion / Ratio / Number,
Divine Proportion, Fibonacci Series and Phi (1.6180339887...)