# The Golden Ratio

## History

The term "golden section" seems to first have been used by Martin Ohm in the 1835 2nd edition of his textbook Die Reine Elementar-Mathematik . The first known use of this term in English is in James Sulley's 1875 article on aesthetics in the 9th edition of the Encyclopedia Britannica. The symbol ("phi") was apparently first used by Mark Barr at the beginning of the 20th century in commemoration of the Greek sculptor Phidias (ca. 490-430 BC), who a number of art historians claim made extensive use of the golden ratio in his works. Similarly, the alternate notation is an abbreviation of the Greek tome, meaning "to cut."

## What is it?

In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities.

## Where is it?

The golden ration is everywhere and used for everything.

The golden ratio in terms of your body is used to identify perfection.The head forms a golden rectangle with the eyes at its midpoint. The mouth and nose are each placed at golden sections of the distance between the eyes and the bottom of the chin. The beauty unfolds as you look further. Even when viewed from the side, the human head illustrates the Divine Proportion.The first golden section from the front of the head defines the position of the ear opening. The successive golden sections define the neck , the back of the eye and the front of the eye and back of the nose and mouth . The dimensions of the face from top to bottom also exhibit the Divine Proportion, in the positions of the eye brow, nose and mouth.

In nature:

The number of petals in a flower consistently follows the Fibonacci sequence. Famous examples include the lily, which has three petals, buttercups, which have five (pictured at left), the chicory's 21, the daisy's 34, and so on. Phi appears in petals on account of the ideal packing arrangement as selected by Darwinian processes; each petal is placed at 0.618034 per turn (out of a 360° circle) allowing for the best possible exposure to sunlight and other factors.

In art:

As the Golden Section is found in the design and beauty of nature, it can also be used to achieve beauty and balance in the design of art. This is only a tool though, and not a rule, for composition.The Golden Section was used extensively by Leonardo Da Vinci. Note how all the key dimensions of the room, the table and ornamental shields in Da Vinci’s “The Last Supper” were based on the Golden Ratio, which was known in the Renaissance period as The Divine Proportion.