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.
See also: Fibonacci, Golden Ratio