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@jlh1182 | 23 March 12 | |
Phideas, the Greek sculptor, and others in ancient Greece and Egypt often use this ratio in designing many of their works of art, Because this ratio has been found to be remarkably pleasing to the human eye, it produces what is called a Golden Rectangle.
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@jlh1182 | 23 March 12 | |
If the short side of the rectangle is 1, the long side will be 1.618. This rectangular shape was close to the pattern used in the designing of the Parthenon of Greece and for many of their numerous pictures, vases, doorways, windowns, statues, etc., and even for certain features of the Great Pyramid of Egypt.
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@jlh1182 | 23 March 12 | |
Many of the things you use are (approximately) patterned after the golden rectanglecredit cards, playing cards, postcards, light switch plates, writing pads, 3-by-5 and 5-by-8 cards, etc.
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@jlh1182 | 23 March 12 | |
Artists such as Leonardo da Vinci, Van Gogh, Vermeer, Sargent, Monet, Whistler, Renoir, and others employed the golden proportion in many of their works. They would take a blank easel and divide it into areas based on the golden proportions to determine the placement of horizons, trees, and so on.
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@jlh1182 | 23 March 12 | |
Another area of great interest is the occurrence of Fibonacci numbers in the spiral arrangement of leaves around a plant's stem (called phyllotaxis). This spiral pattern is observed by viewing the stem from directly above, and noting the arc of the stem form one leaf base to the next, and the fraction of the stem circumference which is inscribed.
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@jlh1182 | 23 March 12 | |
In each case the numbers are Fibonacci numbers. Examples: In an elm the arc is 1/2 the circumference; in beech and hazel, 1/3; apricot, oak, 2/5; in pear and poplar, 3/8; in almond and p*ssy willow, 5/13; and in some pines either 5/21 or 13/34.
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@jlh1182 | 23 March 12 | |
This pattern assures that each leaf will receive its maximum exposure to sunlight and air without shading or crowding other leaves. Not only do we discover this pattern in leaf arrangements, but it is also commonly found in the arrangement of many flower petals. Examples: a lily has 3 petals, yellow violet 5, delphinium 8, mayweed 13, aster 21, pyrethrum 34, helenium 55, and michaelmas daisy 89.
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@jlh1182 | 23 March 12 | |
In the area of very large phenomena when the time period of each planet's revolution around the sun is compared in round numbers to the one adjacent to it, their fractions are Fibonacci numbers, Beginning with Neptune and moving inward toward the sun, the ratios are 1/2, 1/3, 2/5, 3/8, 5/13, 8/21, 13/34. These are the same as the spiral arrangement of leaves on plants
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