Fibonacci numbers and the Golden Number

If we take the ratio of two successive numbers in Fibonacci's series, (1, 1, 2, 3, 5, 8, 13�) and we divide each by the number before it, we will find the following series of numbers:`1

1/1 = 1,   2/1 = 2,   3/2 = 1�5,   5/3 = 1�666...,   8/5 = 1�6,   13/8 = 1�625,   21/13 = 1�61538...

It is easier to see what is happening if we plot the ratios on a graph:

The ratio seems to be settling down to a particular value, which we call the golden ratio or the golden number. It has a value of approximately 1�618034. The golden ratio 1�618034 is also called the golden section or the golden mean or just the golden number. It is often represented by a Greek letter Phi j.

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