Patterns in Nature- Fibonacci Number

Italian mathematician Leonardo of Pisa introduced the Fibonacci numbers. In mathematics, the Fibonacci numbers are generally expressed Fn, which builds the Fibonacci sequence, such that piece by piece number is the amount of the two previous ones, beginning from 0 and 1. That is

F₀=0, F₁=1

And F_n=F_n-1+F_{n-2 ,} for n > 1.

Some starting values of the sequence are below:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, …

The value of F₀=0 is neglected in same older books. In that case, the sequence begins with F₁=1, F₂=1.

and the frequency  F_n=F_n-1+F_n-2  is credible for n > 2 .

Spiral Shape:

The spiral shapes obtained when joining squares with these widths.

We can see the squares fit neatly together.
i.e. 5 and 8 forms 13, 8 and 13 forms 21, and so on.

We found this spiral in nature.

Fibonacci numbers are solidly related to the golden ratio. Binet’s formula conveys the nth Fibonacci number in terms of n and the golden ratio which implies that the proportion of two successive Fibonacci numbers tends to the golden proportion as n increases

Fibonacci numbers arrive unusually of times in mathematics. Applications of Fibonacci numbers carry out computer innovations such as the 1. Fibonacci search technique, 2. Fibonacci heap data structure and 3. Graphs called Fibonacci cubes handled in interrelated parallel and assigned scheme.

Nature:

Fibonacci numbers also appear in biological science, in the area of branching in trees, stem cell analysis, the fruit germinates of pineapple, the flowering of a sunflower and the family chain of honey bees. Kepler finds out the existence of the Fibonacci sequence in nature, using it to clarify the quintuple build of some flowers. Field daisies most often have petals in calculations of Fibonacci numbers.

Family chain of honeybees:

Fibonacci numbers also present in the family chain of honey bees, bestow the following

Always a male bee has one parent whereas a female bee has two. If one detects the pedigree of any male bee, he has 1 ancestor, 2 ancestors, 3 great- ancestors, 5 great-great- ancestor, and so on. This sequence of numbers of ancestors is the Fibonacci sequence. The number of ancestors at each step F_n is the number of female bees, which is F_n−1, plus the number of male bees, which is F_n−2.

It has been indicated that the number of possible parents on the human X chromosome heritage line of a given parent generation also follows the Fibonacci sequence.

A male character has an X chromosome, which he collected from his mother, and a Y chromosome, which he earned from his father. The male polls the “origin” of his X chromosome (F₁=1), and his ancestor’s generation, his X chromosome came from a single ancestor (F₂=1). The male’s mother collected one X chromosome from her mother and one from her father, so two grand ancestors contributed to the male descendant’s X chromosome (F₃=2). The parental grandfather collected his X chromosome from his mother, and the maternal grandmother earned X chromosomes from both of her parents, so three great-grandparents contributed to the male descendant’s X chromosome (F₄=3). etc

The expressway of intramural microtubules organizes the design hierarchy as 3, 5, 8, and 13.