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 (15711630), 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 fivefold symmetry. It appeared again
in the 1980's in quasicrystals, 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.
Source  The
Divine Proportion : A Study in Mathematical Beauty by H. E. Huntley
(1) Page 25
(2) Page 157
(3) Page 158
