Fibonacci number or the Fibonacci sequence is generally starts with 0 or 1 , It is the set of number formed by adding its preceding two numbers. If the Fibonacci sequence is denoted *F* (*n*), where *n* is the first term in the sequence, the following equation obtains for *n* = 0, where the first two terms are defined as 0 and 1 by convention:

*F* (0) = 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 …

In some texts, it is customary to use *n* = 1. In that case, the first two terms are defined as 1 and 1 by default, and therefore:

*F* (1) = 1, 1, 2, 3, 5, 8, 13, 21, 34 …

and so on this process never ends.

The Fibonacci sequence is named after Leonardo of Pisa (also known as Leonardo of Pisa or Fibonacci), an Italian mathematician who lived from 1170 – 1250. In his 1202 book *Liber Abaci*, Fibonacci introduced the sequence to Western European mathematics, although the sequence had been described earlier in Indian Mathematics. It is credited to the sanskrit grammarian known as pingala he

is the one who first mention of the sequence of numbers, sometime between the fifth century B.C. and the second or third century A.D

Fibonacci used the arithmetic series to illustrate a problem based on a pair of breeding rabbits “How many pairs of rabbits will be produced in a year, beginning with a single pair, if in every month each pair bears a new pair which becomes productive from the second month on?” The result can be expressed numerically as: 1, 1, 2, 3, 5, 8, 13, 21, 34 …

If we look around our world we can observe that the nature around us is revolving around these numbers that’s why Fibonacci numbers are of interest to biologists and physicists . we can see many objects and phenomena like branching patterns in trees and leaves, for example, and the distribution of seeds in a raspberry are based on Fibonacci numbers.

**GOLDEN RATIO**

If we write Fibonacci sequence as

1, 1, 2, 3, 5, 8, 13, 21, 34 ,55,89,144………till infinity or limit

1/1=1 , 2/1=2 , 3/2=1.5 , 5/3=1.66666666, 8/5=1.6 , 13/8=1.625 , 21/13=1.6153846153

we can calculate ratio from above method and as we calculate the ratio of larger number it will start to approach GOLDEN RATIO which is given below.

The Golden ratio is approx 1.6180399887…and so on