**From the very beginning of the human civilization and also in modern days Fibonacci plays a vital role in curving the life of humanity through its various applications in today’s seamless and fast pace world. Its Numbering pattern is followed everywhere around us its number sequence or pattern starts from 1 or 0 which is also apparently the basic binary code. Followed by a one, and proceeds based on the rule that each number (called a Fibonacci number) is equal to the sum of the 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 …

The Fibonacci sequence is related to the golden ratio, a proportion (roughly 1:1.6) that occurs frequently throughout the natural world and is applied across many areas of human endeavour. Both the Fibonacci sequence and the golden ratio are used to guide design for architecture, websites and user interfaces, among other things.

Information About the discovery of Fibonacci

A Sanskrit grammarian, Pingala, was the first person to mention of the sequence of numbers, sometime between the fifth century B.C. and the second or third century A.D. Since Fibonacci introduced the series to Western civilization, it has had a high profile from time to time.

After that a well-known Italian Mathematician known as Leonardo Pisano or Fibonacci between 1170-1250 used this arithmetic series to explain its practical usage where he used a pair of breeding rabbits.

**Fibonacci Represents life**

Rabbits always give birth to pairs, and each pair consists of one male and one female.

Think about it — two new born rabbits are placed in a fenced-in yard and left to, well, breed like rabbits. Rabbits can’t reproduce until they a¬re at least one month old, so for the first month, only one pair remains. At the end of the second month, the female gives birth, leaving two pairs of rabbits. When month three rolls around, the original pair of rabbits produces yet another pair of new-borns while their earlier offspring grow to adulthood. This leaves three pairs of rabbit, two of which will give birth to two more pairs the following month.

The order goes as follows: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and on to infinity. Each number is the sum of the previous two. This series of numbers is known as the Fibonacci numbers or the Fibonacci sequence.

Fibonacci is the answer of all secrets of this universe as it encompasses all the topics starting from the arrangement of our galaxy or milky way to the DNA of human beings .

**Its application on modern day world**

In writing programming language:- Suppose we’re writing a computer program to search a sorted array for a particular value. Usually the best method to use is a binary search. But binary search assumes it’s the same cost to read from anywhere in the array. If it costs something to move from one array element to another, and the cost is proportional to how many array elements you need to skip over to get from one element you read to the next, then Fibonacci search works better. This can apply to situations like searching through arrays that don’t fit entirely in your computer’s cache so it’s generally cheaper to read nearby elements that distant ones.

**Its application in Music:-**

In a scale, the dominant note is the 5th note of the major scale, which is also between the 8th note to all 13 notes that comprises of the octave. This provides proof Fibonacci numbers in key musical relationships. Interestingly, 8/13 is .61538, which approximates phi

**Application in Daily Life:-** The Fibonacci numbers are Nature’s numbering system that prevails every where

starting from leaves of the plant to the pineapple trees

**CONCLUSION:**

Thus Fibonacci Number system encircles our entire life cycle and a source of that mathematics which affects our day to day life and an integral part of Universe which has the capacity to define each and every aspect of human life very clearly .