The Golden Ratio

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The Golden Ratio Certain pictures, objects, and animals appeal to the human mind more than others. Proportions and images of symmetry often contribute to our fascination with them. Often, when examined carefully, you may find a common “coincidence” between man made objects and those found naturally in nature. This fluke, however, may be used to ascertain various mathematical relationships between these objects. This paper will introduce the golden ratio and weigh its significance on math, art, and nature. 1.6180339887…. has been given many names varying from the “golden ratio” first coined by the Greeks, to the “golden rectangle” and “golden section”, “phi” named after Phidias a renowned Greek sculptor, as well as the “divine proportion” conceived by Leonardo da Vinci. (Blacker, The Golden Ratio) Simply put, the golden ratio is the length to width of rectangles used in art and nature. This ratio is considered to be the most agreeable arrangement, mathematically and artistically, to the eye. Perhaps the first to use the golden ratio were the Egyptians. Many (if not all) of the pyramids were made with the golden ratio kept solely in mind… as if they were made only using the ratio. Later, the Greeks began using it in their architecture as well as their sculptures. Phidias and others popularized the golden ratio by basing their achievements on it. The Parthenon, specifically, as well as several other buildings and sculptures were the subject of which the ratio has left its mark. The Greeks and the Egyptians were by far not the only people to have been affected by the number. Famous painters and mathematicians have also recognized the ratio’s significance. Perhaps the most famous and blatant use of the gol... ... middle of paper ... ...rt. New York: Dorling Kindersley, 1994. Blacker, Steve and Jeanette Polanski and Marc Schwach. “Golden Ratio: Fibonacci in Nature.” Dec. 8, 1999. http://www.geom.umn.edu/~demo5337/s97b/spiral.html Blacker, Steve and Jeanette Polanski and Marc Schwach. “Golden Ratio.” Dec. 8, 1999. http://www.geom.umn.edu/~demo5337/s97b/art.htm Brown, Kevin. “Math Pages: The Golden Pentagon.” Dec. 11, 1999. http://www.seanet.com/~ksbrown/kmath153.htm “Fibonacci & The Golden Ratio.” Dec. 8, 1999. http://www.aegsp.br/hs/fib/ Knott, Dr. Ron. “Fibonacci Numbers and Nature.” Dec. 8, 1999. http://www.ee.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html#Rabbits Snyder, Brian Joseph. “The Golden Mean – The Golden Section.” Dec. 7, 1999. http://www.netreach.net/people/waterboy/phiratio/ Stokstad, Marilyn. Art History. New York: Prentice Hall, 1999.

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