Running head: FIBONACCI NUMBERS AND THE GOLDEN RATIOFibonacci Numbers and the Golden Ratio in Music, Art, and NatureNameInstitution AffiliationFIBONACCI NUMBERS AND THE GOLDEN RATIO2Fibonacci Numbers and the Golden Ratio in Music, Art, and NatureThe Golden ratio, which is also known as Golden mean, divine proportion, or Golden section isthe resultant digit after dividing a line in two sections whereby when the longer area is dividedby the shorter one is also equivalent to the entire length divided by the longer part. Usually, it issymbolized by phi, which is rounded off to 1.618 (Markowsky, 1992). Equally, phi can bederived through the Fibonacci sequence, which is a series of numbers that are attained by addingtwo numbers to get the next. Thus, phi is arrived at by dividing the number by the one precedingit.Application in the Real WorldThe Golden ratio has been applied in Leonardo Da Vinci's paintings, for example, in TheAnnunciation and Madonna. In The Annunciation the painting is on a frame of 1:sqrt(5),which fits to the Golden rectangle. The 0.618 lines were used to mark the most important parts ofthe painting. When they are geometrically ...
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