Friday, January 20, 2012

The Golden Ratio

Leonardo DaVinci extensively used mathematics in his artwork. The dimensions of the room and the table of his "The Last Supper" and his portrait of the Mona Lisa were based on the Golden Section, which was known in the Renaissance period as The Divine Proportion. The golden ratio is referred to as "phi" and is approximately equal to 1.6180. This ratio can be found in architecture, including the pyramids, and throughout nature: the spiral in the nautilus, snails, pine cones, pineapples, and sunflowers. Even your fingers have elements of the golden ratio.  
Another Italian mathematician Leonardo Pisano Bigollo, best known as Fibonacci, demonstrated that the golden ratio consists of the sum of the two numbers before it as shown below. 
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, ...

Fibonacci found that by dividing  any number in his sequence by the one before it, for example 21/13 or 987/610, the quotient is always close to 1.6180, the golden ratio. 








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