International Journal of Engineering Science Invention
ISSN (Online): 2319
–
6734, ISSN (Print): 2319
–
6726
||Volume 6 Issue 9|| September 2017 || PP. 07-14
7 | Page
The Fibonacci Numbers and Its Amazing Applications
*Sudipta Sinha
Assistant Professor Department of Mathematics Burdwan Raj College,Burdwan,West Bengal,713104
Corresponding Author: Sudipta Sinha
Abstract:
Fibonacci sequence of numbers and the associate
d “Golden Ratio” are
manifested in nature and in
certain works of art. We observe that many of the natural things follow the Fibonacci sequence. It appears in
biological settings such as branching in trees, phyllotaxis (the arrangement of leaves on a stem), the fruit
sprouts of a pineappl
e
, the flowering of an artichoke, an uncurling fern and the arrangement of a pine cone's
bracts etc. At present Fibonacci numbers plays very important role in coding theory.
Fibonacci numbers in
different forms are widely applied in constructing security coding.
Keywords:
Fibonacci Numbers, Golden ratio, Coding, Encryption, Decryption
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Date of Submission: 05-08-2017
Date of acceptance: 13-09-2017
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I.
Introduction
The Fibonacci numbers were first discovered by a man named Leonardo Pisano. He was known by his
nickname, Fibonacci. The Fibonacci sequence is a sequence in which each term is the sum of the 2 numbers
preceding it. The Fibonacci Numbers are defined by the recursive relation defined by the equations F
n
= F
n-1
+
F
n-2
for all n
≥
3 where F
1
= 1; F
2
= 1 where Fn represents the nth Fibonacci number (n is called an index).
The Fibonacci sequence can elaborately written as {1,1,2,3,5,8,13,21,34,55,89,144,233
…….}
.
One of the most common experiments dealing with the Fibonacci sequence is his experiment with rabbits.
Fibonacci put one male and one female rabbit in a field. Fibonacci supposed that the rabbits lived infinitely and
every month a new pair of one male and one female was produced. Fibonacci asked how many would be formed
in a year. Following the Fibonacci sequence perfectly the rabbits reproduction was determined...144 rabbits.
Though unrealistic, the rabbit sequence allows people to attach a highly evolved series of complex numbers to
an everyday, logical, comprehendible thought.Bortner and Peterson (2016) elaborately described the history and
application of Fibonacci numbers.
II.
Fibonacci Sequence In Nature
Fibonacci can be found in nature not only in the famous rabbit experiment, but also in beautiful flowers
(Internet access, 12). On the head of a sunflower and the seeds are packed in a certain way so that they follow
the pattern of the Fibonacci sequence. This spiral prevents the seed of the sunflower from crowding themselves
out, thus helping them with survival. The petals of flowers and other plants may also be related to the Fibonacci
sequence in the way that they create new petals (Internet access, 10).

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