Monday, 10 September 2018

Fibonacci


By @Rishi_Babbar | 10 September 2018 | (Actual Date ~ 1996-98)

Hello readers… following is the speech I prepared years back for a competition when I was in secondary school. Hope you enjoy reading and also gain knowledge regarding this wonderful topic.

“At the outset of my talk I would like to define Mathematics. It is the name of a group of sciences concerned with numbers, quantity, shape and place and their various relationships. Mathematical ideas help us in understanding the world in which we live. It should be visualized as the vehicle to think, reason, analyse and articulate logically.

When we observe various phenomena in nature, for example division of a cell, reproduction of unicellular organisms like bacteria and amoeba, arrangement of branches leaves and flowers around the stem, arrangement of petals in a flower, disintegration of atoms of a radioactive element, all are found to be following some fixed number pattern. Exploring and discovering these number patterns was always a primary source of fascination for humans. A given number pattern, which is a set of numbers is called a sequence, which can be thought of a list. A sequence can be defined y some rules or rules or can be stated in words.

Among the many sequences known to us that mathematicians have studied, surely, none is more fascinating than “Fibonacci Sequence”. This sequence was introduced by an Italian mathematician, Leonardo of Pisa, also known as Fibonacci, born in 1180 AD. His work was published in the year 1202 AD in the book titled “Liber Abaci” meaning “Book of Counting”. Through this he introduced the Hindu-Arabic numerals from 0 to 9 into western Europe and described the joys of learning the art of nine Indian figures and the symbol zero – ‘0’. Learning about Leonardo’s findings, the Roman Emperor Frederick II invited Leonardo. Frederick himself was known as the “wonder of the world” for his patronage of science. His works propounded a series of problems which Leonardo solved by ‘trial and error’ methods. His solutions to the problems were a combination of ingenuity and accuracy.

In 1220, Leonardo produced a brief work on geometry the “Practica Geometriae” meaning practice of geometry. This was based on Euclid’s elements. In 1225, his works “Liber quadratorum” meaning book of square numbers was published which ranks him as the major contributor to the number theory, But his name is known to modern mathematics mainly because of “Fibonacci Sequence”.  The famous “Fibonacci Sequence” emerged when the growth of a colony of rabbits was being studied. The growth followed the sequence that is now called the “Fibonacci Sequence”. This sequence is such an interesting one that once person becomes aware of the numbers in the Fibonacci Sequence the numbers seem to popup everywhere. Several kinds of growth processes follow the same sequence.

Well… I’ll end your eagerness.
What is this Fibonacci Sequence?
It is a set of numbers in which each number from third onwards is obtained by adding the previous two. Any sequence which obeys this rule is a Fibonacci Sequence, no matter what the first two numbers are: 1,1,2,3,5,8,13, 21, 34, …… or 4,7,11, 18, 29, ….
What’s the specialty about this sequence?
The numbers…. and Fibonacci ratio, which is the ratio of two successive terms in Fibonacci Sequence. This is the first, recursive number sequence known in Europe in which the ration between the two or more successive terms can be expressed by a formula. This fascinating and interesting sequence was given by Leonardo Fibonacci when he was just 22. But the term “Fibonacci Sequence” was coined in 19th century by a French mathematician Edward Lucas. Thereafter scientists began to discover the numbers of this sequence in nature. As a simple example, next time, if you pick up a sunflower head and count spirals, you’ll observe that the head has 55 spirals in the clockwise and 34 in anti-clockwise direction. Look at a pine cone which has 13 anti-clockwise and 8 clockwise parts, both follow Fibonacci ratio numbers from this sequence arise in many surprising contexts including the structure of bee-hive, the population of a rabbit warren, white-black notes on a piano keyboard. Not only this, many growth processes in nature govern the sequence.

This great mathematician died at the age of 70 in 1250 AD. If you would like to find out more about other facts such as the golden ratios, the golden rectangle, etc. many mathematical, recreational books have chapters devoted to it, which would deepen your ideas for this exciting topic.”

Thanks for reading … 

4 comments:

Bahubali - The Vegetarian

Vegan Bahubali LEARN MORE ABOUT VEGETARIANISM HERE : 1. http://spiritualdatabase.blogspot.in/2015/02/great-quotations-on-vegetarianism...