Golden section

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Golden Section

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"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."

-- Johannes Kepler [1571-1630]

Whenever an artist determines the visually pleasing position or placement of the major parts of his work , he is consciously or perhaps, unconsciously, using the Golden Section. The Golden Section is a special ratio that was derived during 5th century BC, also known as the Golden Age of Greece. During this time, the Greeks were commonly known for their beautiful art and architecture The Golden Section is also called the Golden Ratio, Divine Proportion or the Golden Rectangle.Euclid revealed a visually pleasing geometric proportion which has been regarded as the formation of accepted beauty by many art theorists (and mathematicians). It is a ratio between the two dimensions of a plane figure or the two divisions of a line, such that the smaller element is to the larger as the larger is to the whole: the Golden Proportion. The Golden Section are most significantly used in the design of the Parthenon, located in Athens, Greece. Ictinus and Callicrates designed the structure using mathematical principles. For example, the façade of the Parthenon was composed using two large root five rectangles and four smaller ones. The ratio of the length of the building to the height of the face is phi, the Golden Section. Lastly, there is an even number of pillars along the front, which numbers eight, and an odd number along the sides, numbering seventeen.

The Parthenon for these reasons, has become to be known as the "perfect building." These unusual mathematics properties are key reasons for the building’s aesthetic beauty and attention received for ages. The Golden Section relationship asserts a natural balance, a dynamic symmetry.
Another interesting part of the Golden Mean is its presence in the proportions in nature, specifically the human body. For example, the length of the first finger joint to the length of the next two joints is equal to the length of the two joints to the length of the whole finger. Similarly, the length of the middle finger to the length of the palm is equal to the length of the palm to the length of the whole hand. Lastly, the length of the hand to the length of the forearm is equal to the length of the forearm to the length of the finger to the elbow. This amazing discovery is the main reason for the beauty of the human figure and the patterns commonly found in nature, art, and architecture.

        

        

        

        

        

 © 2001-2003 Radoslav Jovanovic              translated: D.Filipovic   created:  January 2003.