FIBONACCI SEQUENCE! THE MAGIC!!!

Though mathematics is an interesting and beautiful subject, most of us find it difficult to learn. We often learn mathematics to do calculations and learn formulas to get good grades in the exams. Mathematics is a wonderful subject which we tend to apply in our day-to-day life. If you see maths through a different dimension, it will be as interesting as social media. We learn so many formulas and theorems, but where do we apply them? Think and come to a solution to make mathematics an interesting one. To prove mathematics an interesting subject, here come the Fibonacci numbers. Most of us have heard it once or twice in our classes when our teacher says about it. If you love to play with numbers, then Fibonacci numbers are the one. Let’s see how interesting these Fibonacci Numbers are!!

The Fibonacci Sequence in Nature

Fibonacci numbers are numbers, such that each number is the sum of the two preceding numbers starting from 0 and 1. The Fibonacci numbers or Fibonacci sequence are first used in the book, Liber Abaci, by Fibonacci which is used in the calculation of the growth of the rabbits. The Fibonacci numbers are closely related to the golden ratio. The ratio of the two consecutive Fibonacci numbers gives the golden ratio as n increases. {Golden Ratio: 1.61803398875}. Though, Liber Abaci contain the earliest description outside India, Indian mathematicians are the ones who described Fibonacci sequence as early as the sixth century.

Fibonacci Sequence

The Fibonacci day is celebrated on November 23rd every year. If we write it in mm/dd format, 11/23; it is also a Fibonacci number. The name Fibonacci is named after its inventor, Leonardo of Pisa, commonly known as Fibonacci was an Italian Mathematician, who was famous for his invention in the history of mathematics.

Leonardo of Pisa, commonly known as Fibonacci (1170 – 1250)

Let’s see the Fibonacci sequence with the example of rabbit, A farmer put a pair of rabbits on a closed surface. How many rabbits can be produced from the pair in a year, if it is that every month each pair produces a new pair which from the second month on becomes productive? The solution is the Fibonacci sequence. The sequence will go on like   1, 1, 2, 3, 5,….. and so on.

FIBONACCI SEQUENCE IN NATURE!!

  • In some flowers, the petals are arranged in the Fibonacci sequential arrangement which is enough to prove that Fibonacci sequences are available in nature too.
  • In the branches of plants, the leaves are spirally arranged in the Fibonacci sequence arrangement. In small plants, it will be 5 or 8. In larger ones, it will be 8 or 13 based on the growth of the plant.
  • The pattern of the seeds within the sunflower follows the Fibonacci sequence (1,1,2,3,5, …..).
The nature of design: the Fibonacci sequence and the Golden Ratio -  Cleveland Design

Fine! Till now, we saw what is a fibonacci sequence, and who is the inventor and where can we see this fibonacci series. Now, shall we see where these fibonacci sequence are used practically? Yeah! Come on!

IN MATHEMATICS,

  • The Fibonacci numbers occur in the sum of the shallow diagonals of Pascal’s triangle.
Fibonacci sequence and Pascal’s triangle
  • The Fibonacci sequence is also used in the Pythagoras theorem. The hypotenuse of the triangle can be a Fibonacci number.
  • The Fibonacci sequence is also used in the network topology for parallel computing.

IN COUMPUTER SCIENCE,

  • The Fibonacci numbers are important in the analysis of algorithms (computational run-time analysis) of Euclid’s algorithm.
  • Its also used in the common factor tree method that is called a binary tree method which is the Fibonacci number minus one.
  • This Fibonacci sequence also used in the game called poker, it is a step in the game development.

Fibonacci sequence are used not only in these two fields but also in many other fields. To put it simply, I have given these two fields. As we saw earlier, fibonacci sequence can also be seen in nature. While contructing tall buildings, climb up and see from the top, this is also an example of a fibonacci sequence.

Algorithms 101: Climbing stairs in JavaScript | by Joan Indiana Lyness |  JavaScript in Plain English

These are the various interesting facts in the Fibonacci sequence. It’s just a small part of mathematics. If we take an interest in various parts or topics in mathematics, we can make maths an interesting one. Mathematics is an ocean, where Fibonacci sequence is a small fish in it. Let’s try to catch various fishes like the Fibonacci sequence and make our lives a great one. If you find it interesting, just do some more research and excite by yourself like how I got excited!!

Reference links;

https://www.mathsisfun.com/numbers/fibonacci-sequence.html

http://www.eniscuola.net/en/2016/06/27/the-numbers-of-nature-the-fibonacci-sequence/