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 …
