How the Golden Ratio and Fibonacci Numbers Connect

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.