### Fibonacci, the Golden Mean and Nature

The Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 is an infinite sequence, in which any number can be found by adding the previous two numbers in the sequence. For example, the next number in the sequence would be 34+55= 89.

There are many fascinating mathematical properties of the Fibonacci sequence. For example, no two consecutive numbers in the series have any common factors, 144 which is the twelfth number is the only square number in the entire sequence and the sum of any ten consecutive numbers is always divisible by eleven.

More interestingly,

Every 3rd Fibonacci number is divisible by 2

Every 4th Fibonacci number is divisible by 3

Every 5th Fibonacci number is divisible by 5

Every 6th Fibonacci number is divisible by 8

Every 7th Fibonacci number is divisible by 13

Every 8th Fibonacci number is divisible by 21

### The Golden Mean

If you divide a number from the sequence by the previous number, you get the Golden Mean. For example, 55:34= 1.618. This is the perfect harmonic ratio, and can be seen anywhere in the growth spirals of pinecones, flower petals and seeds and the branching pattern of trees. And the bigger the numbers, the more perfect/accurate the ratio. But it will never get to 100% perfect, its an infinite number. Its a spiral!