Perfection exists in nature even if we do not realize it. The ancient Greeks were the first to discover the Golden number which represented perfect harmony. This was considered to be a divine proportion.
ϕ is the basis for the Golden Ratio, Section or Mean
The ratio, or proportion, determined by ϕ pronounced as Phi (1.618 …) was known to the Greeks as the “dividing a line in the extreme and mean ratio” and to Renaissance artists as the “Divine Proportion“. It is also called the Golden Section, Golden Ratio and the Golden Mean.
Ancient Egyptians and Ancient Greeks
The Egyptians may have used ϕ in the design of the Great Pyramids. The Greeks are thought by some to have based the design of the Parthenon on this proportion.
Phidias (500 BC – 432 BC), a Greek sculptor and mathematician, studied ϕ 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.
The Fibonacci Series was discovered around 1200 AD
Leonardo Fibonacci, an Italian born in 1175 AD 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 ϕ and the Golden Mean. His most notable contribution to mathematics was a work known as Liber Abaci where he wrote a simple numerical sequence that is the foundation for an incredible mathematical relationship behind ϕ.
Starting with 0 and 1, each new number in the sequence is simply the sum of the two before it.
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, . .
The ratio of each successive pair of numbers in the sequence approximates ϕ (1.618. . .) , as 5 divided by 3 is 1.666, and 8 divided by 5 is 1.60…
After the 40th number in the sequence, the ratio is accurate to 15 decimal places.
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”, 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.
ϕ and astrology
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 ϕ was not used until the 1900′s
Mark Barr was an American mathematician who, according to Theodore Andrea Cook, in about 1909, gave the golden ratio the name of ϕ.
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