![]() ![]() ![]() (and 3 divided by 2 equals 1.5), but 21 divided by 34 equals 0.6176. For example, 2 divided by 3 equals 0.6666. If you take the quotient of any two numbers in the Fibonacci series, you will find that the further you go up the line, the closer the value converges on the "perfect" ratio. It is permissible at this point to ask what all this has to do with the Golden Ratio, and therein lies the beauty. This deceptively simple-looking series is obtained merely by sequentially adding numbers which are the sum of the preceding two. Fibonacci reasoned that, if the rabbits reached maturity two months after birth and produced an additional pair every month thereafter, the total population of rabbit pairs would increase monthly according to the series 1, 2, 3, 5, 8, 13, 21, 34. ![]() The "Fi" part of his name meant "son of." The Bonacci part meant "simpleton."Īlthough history does not record the mental acuity of Fibonacci's father, it does relate that the boy took an early interest in the number of rabbits that could be raised in a year if one began with a single pair. Historically, credit for recognition of the peculiar mathematical properties of this ratio must go to a 13th century Italian known as Fibonacci. The earlier column told only half the story of the Golden Ratio, however. It is also found in nature, reflected in essentially every spiral form from a snail shell to the arms of a galaxy. Thus, the shape seems to be subliminally pleasing to the human eye, as witnessed by the many ways in which it is used in art and in construction. Rectangles with sides proportioned 0.618034 to 1 (or 1 to 1.618034) are often the shape taken by such commonplace items as picture frames and playing cards. To recapitulate briefly, the Golden Ratio consists of the two numbers 1.618034 and 0.618034, each of which is the reciprocal of the other. The interest shown seems to justify a sequel. Seldom has an article appearing in this space generated the volume of reader response as did last month's column on the Golden Ratio. ![]()
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