Fibonacci Sequence

The Fibonacci Series is 0,1,1,2,3,5,8,13,21,34,55,......

This Series is generated by adding two number before it :

for example :
5 is found by adding two numbers before it that is 2+3.

Similarly 8 is found by adding two numbers before it that is 5+3.

and so on..

The Fibonacci Sequence can be written as a rule such as
 X_n=X_n-1 + X_n-2
For example : X_n-1=21 and X_n-2=13 Therefore X_n becomes 34.

When we  make a square as shown below we get a Spiral shape :

Golden ratio : If we take two successive number Fibonacci number we get a known as Golden Ration which has the approximate value as  1.61803399....
Bigger the pair of Fibonacci Numbers, the closer the approximation.

The symbol for Golden ration is φ (phi).


Fibonacci in Nature: 

The Fibonacci appears in the smallest, to the largest objects in nature. It is a way for information to flow in a very efficient manner.
some of the images below shows the Fibonacci sequence in Nature


Fibonacci sequence in Cancer Cell Division

Fibonacci sequence in Galaxy

Posted in: Division, Formulas, Geometry, Maths