12
The Relationship between Fibonacci Numbers and the Golden Ratio
Leonardo Fibonacci discovered the Fibonacci Sequence - a series of numbers where adding the two previous numbers in the sequence provides the next number. The sequence begins with 1, 1, 2, 3, 5, 8, 13, 21, 34, 55....
The Golden Ratio, or Phi, is a number - approximately 1.618. The ratios of Fibonacci numbers converge on Phi. The ratios of successive Fibonacci numbers are as follows:
1/1 = 1.000000
2/1 = 2.000000
3/2 = 1.500000
5/3 = 1.666666
8/5 = 1.600000
13/8 = 1.62500
21/13 = 1.615385
34/21 = 1.619048
55/34 = 1.617647
89/55 = 1.618182
144/89 = 1.617978
233/144 = 1.618056
As you can see - the ratio of two successive Fibonacci Numbers moves higher and lower, but gravitates closer and closer to the Golden Ratio - 1.618.
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