Hey guys, today we're going to look at
a number called the Fibonacci number
and how this is a Hindu number
which originally came from ancient India
and this Fibonacci number is the basis
of life itself. Now according to
historians, the Fibonacci number
was discovered around 1200 A.D -
that's about 800 years ago
by an Italian called Fibonacci.
Fibonacci was not an Indian and he was
also
not a Hindu, he was an Italian and he was
a
Catholic so why is
Fibonacci a Hindu number?
First, we need to understand what is
a Fibonacci number.  Fibonacci number
is a series of numbers
like this. You may or may not include
zero
and you can start: 1, 1,
2, 3, 5,
8, 13...
What is so special about this series? And
this series
goes forever. Why not
just make up another series like this?
For example, why don't we say
2, 4, 6, 10,
16? What is different between
this series and this
Fibonacci series? Fibonacci number
was not a random number made up by
human beings. It is the number
of the Gods and this is the difference
between life and death.
What do i mean by that? Why do I say that
the Fibonacci
number is the number of the Gods? To
understand the Fibonacci number and its
connection to
life, let's take a look at one
cell. Let's just take one cell
and let's assume that this cell has just
been born.
Before this there is nothing and
then this cell has just been born.
After two minutes, the cell becomes fully
mature
and after the cell becomes fully mature
it gives birth to a new cell
every minute. So in the first minute the
cell is brand new.
In the second minute the cell is one
minute old,
i'm putting one line for one minute old.
In the third minute
the cell would have been fully mature, so
i'm putting two lines like this.
Now it would have given birth to
another cell. Now in the fourth minute,
this cell is fully mature, so it will
give birth to
another cell, but this cell
would be one minute old. In the fifth
minute
the cell is already mature, so it gives
birth to
another one. Now this cell would be
one minute old, this cell would be two
minutes old.
Because this is also mature this gives
rise to
another cell. Now,
what happens at the sixth minute?
You can solve this problem in two
methods, you can
go on drawing circles and try to figure
out how many cells will be there
at the end of six minutes. Or
you may have recognized a pattern
already. Here
this is 1 and here
this is 1.  The next level is 2.
This is actually 1 + 1. This is
2. 
And in this level you see 3 cells
which is actually
1 + 2.  This is why this is 3
and at this level you can see this there
are a total of 5
cells and you you can see that it is 2
plus 3 that's 5.
So at the sixth minute your answer
would be 8 because 3+5
is 8. This
is the Fibonacci series and you may ask:
do cells really replicate
this way? Do cells multiply or divide
like this? This is called the
asymmetric cell division
under optimal conditions. You can
see the Fibonacci number not only at
cell level,
you can even see it in DNA
SUPRA CODE. Now what is the dna supracode?
It is the organization of nucleic acid
bases
in a dna sequence. Now
you can see the Fibonacci number in
micro level
in various places in a living organism. 
For example, you can
also see it in the order of replication
of dna in living cells. So
you do see that there is a connection
between
the Fibonacci numbers and life itself.
So Fibonacci number holds the key
to life but do we need a microscope
to see the Fibonacci number?
Let's take a look at something we can
see.
Assume that i'm going to plant the seed
in the soil, okay?
so this is a seed that i'm planting in
the soil.
The first day, the root will grow
a little bit and the second day
the root grows a little bit longer.
After that on the third day, it will
still grow longer,
but will split into two.
And on the fourth day,
one will just grow longer while the
other
will split
like this. This is kind of a weird
drawing and who is going to actually
look at how seeds grow
in real time. Believe it or not, this is
what
ancient hindus were studying what is the
point of this diagram?
The point is, if you take it at any
timeline,
it will match the Fibonacci number. So
here you can see
1, here you can see 1, here you can
see 2,
here you can see 3 and the root will
grow further
based on the Fibonacci number.
And not just the root,
As above, so below.. so if you look at the
stem
or the trunk or shoot, again you will see
the same pattern
of Fibonacci numbers growing. So you can
see the Fibonacci number
in roots above the ground in stems or
shoot.
You can also see it in leaves you can
see it in flowers,
you can also see it in seeds. If you look
at
a sunflower, there are seeds arranged
in the middle of the flower and they
will always
be in Fibonacci numbers. If you take
a pineapple, and if you look at the
scales,
you'll be surprised because the scales
will
always be in 5, 8,
13 or 21. All of these
are Fibonacci numbers so you can
understand
that the fibonacci number not only
occurs
at micro level, it also occurs
at macro level and this is not just
limited to
a plant or a tree. When the seeds
disperse,
even the seeds fall in fibonacci
pattern.
So we're looking at an entire
orchard that is formed on the basis
of Fibonacci numbers, an entire forest
will be designed based on the Fibonacci
number.
This is why i call Fibonacci
as the number of the gods but
why do I call this amazing number, the
Fibonacci number
as a Hindu number? Fibonacci number was
discovered
800 years ago by an Italian
who was a Catholic but
why do i call it a Hindu number?
Let me clear the board and let me
explain it to you.
So Fibonacci
discovered this number around
1200 A.D,
but 50 years before Fibonacci there was
a great
Sanskrit poet in India called
Hemachandra
around 1150 A.D.
He was teaching some students about how
to compose
poetry. In Sanskrit
syllables there are short syllables
and there are long syllables. The short
syllable
is called Laghu and it takes
one beat of time and the long syllable
is called Guru and it takes
two beats of time. Now,
one of his students asks a question
to Hemachandra. He says 'there are
8 beats
to fill up in a poem.
How many combinations are there
to fill using Laghu
and Guru? So think about this, so you have
eight spaces you can fill.
So you can take all short, for example.
And you can also do all long
for example. And you can also do short,
long, short,
long, and you can do a long, long, short.
What do you think
is the answer to this question? How many
combinations do you think there are
to be filling up these 8 spaces?
Believe it or not, Himachandra gives an
instantaneous reply. He starts
by saying, add 1 + 1 and keep
going
and keep adding the consecutive numbers
and the 8th
number you get is the number of
combinations you can use
to fill up these 8 spaces. So he
actually
gives the correct answer that the 8th
Fibonacci number is the number of
combinations
you can use to fill up these spaces.
At this point,
two things could shock you: 1) if you
know
enough Indian history, you know
Hemachandra was not a Hindu
poet. He was a Jain poet he belonged to
Jainism. The second thing that could
shock you
is that Hemachandra was only
50 years before Fibonacci. Fibonacci
was publishing his book around 1200 A.D
and Hemachandra was giving out this
answer to his
students about 1150
A.D, just about 50 years before Fibonacci.
and that's not a big deal, maybe these
two people were contemporaries
and they both had the same thoughts.
But I'm shocked by the 3rd aspect:
why did Hemachandra give
an instantaneous reply? And
why was the answer so brief
without explaining how he came to that
conclusion?
Why did Hemachandra did not take his
time
to explain how he arrived at the
right answer to such a complicated
question?
Think about this when somebody asks you
here's a right angle triangle
and one side is 1 foot
the other side is also 1 foot
what is the length of the hypotenuse?
To most people, they would
really answer this as √2 and that
would be the
end of the conversation. Because we
have 2500 years of
Pythagoras theorem before us so we don't
find the necessity
to explain the same thing over. We don't
really say this is one squared and this
is one squared
and if you add both the squares then it
would be the result of it.
We don't really explain it, we just give
out the answer
because we are sitting with
2500 years of Pythagoras
before us. This is exactly what is
happening
with Hemachandra. Hemachandra is not
explaining how he came to this
conclusion,
he is merely giving out the solution
because Hemachandra did not discover the Fibonacci number. Hemachandra  was sitting on
thousands of years of knowledge of
fibonacci numbers
before him. The ancient Hindus knew about the Fibonacci numbers
thousands of years before Hemachandra.
At this point, some of you will say: Now
Praveen, this is why
YouTube bans you, this is why Facebook
bans you, this is why Twitter bans you,
because you exaggerate things. It's
one thing
if you say Hemachandra gave the right to
answer
about Fibonacci number before Fibonacci
in
1150 A.D, but why are you exaggerating
this
and saying that there was
thousands of years of knowledge about
Fibonacci numbers
before Hemachandra? This is why
you get banned because you
exaggerate
Indian history. I have actual proof of
this,
there was a great mathematician
called Pingala, he was a
Hindu mathematician, he was
living around 200 B.C.
Some scholars even believe that he was
living much
older in time around 500 B.C, but most
historians accept that he was living
around 200 B.C and Pingala
actually put the Fibonacci numbers
in a text and he called the Fibonacci
number
as 'Maatra Meru'.
This is the original name
of the Fibonacci numbers. If you look up
the text of Pingala, you will be
astonished because
Pingala clearly lays out how the
Fibonacci
numbers work 2200 years ago, and not only that
Pingala also discovered the
Pascal's Triangle. Now, pingala
really lays out how short syllables and
long syllables
fill up these spaces and he clearly
explains
the Fibonacci series as we know it today.
 Maybe this is too dull for you - short
syllable,
long syllable, Sanskrit, the old language.
Maybe this is just too dull for you. If
you're young,
you may think this is just too boring, so
let's switch
gears. So let's say you want to do
some competitive exam, you want to take
SAT, GRE, IIT exam, you want to
do IPS or IAS and you will
encounter a question like this. So these
are the steps
in a staircase and you can
take 1 step
or you can take 2 steps.
How many combinations can you use,
if there are a total of 10 steps?
The answer is the 10th Fibonacci number.
This is a very complicated question you
will
encounter today, if you're taking a very
advanced
exam. Believe it or not this is actually
used
in computer programming this is called
Dynamic
Programming,
programmers use this.
And the answer to all these complicated
questions that you will face today
were given by a Hindu mathematician
2200 years ago. This is
why I call the Fibonacci number
as a Hindu number which originated
in ancient India. Now you know that
Fibonacci
number was originally a Hindu number,
but did Fibonacci steal this number,
hide the sources, to promote himself?
No, he did not. Why?
Because his name is not Fibonacci
at all. It's very interesting because
Fibonacci
has written an amazing book called the
Liber Abacci. It transformed the way
Europe was doing business and
mathematics,
but Fibonacci never spoke about
himself. In fact, most scholars
are still debating about what his
original name was, most people think
his original name was Leonardo
Bonacci but they're still not sure.
And Fibonacci was a very modest person
and he did not promote himself. Even
better,
Fibonacci gave full credit
to the Hindu mathematical system.
In fact in his book he called
this new system as 'Modus Indorum'
which means the 'Method of the Indians'.
In fact, Fibonacci goes one step further,
he not only praises Hindu mathematical
system,
he even says when you compare the hindu
mathematical system with
Arabs and Pythagoras,
Pythagoras seems almost like a mistake.
This is incredible because Fibonacci is
saying
when you compare Pythagoras, who's
considered the father of mathematics by
many people,
when you compare Pythagoras with the
Hindu system
Pythagoras seems almost like a mistake.
If somebody walks up to you and he says
Pythagoras is a mistake
you would think this person is nuts, but
it is
Fibonacci who is saying this. He was a
great mathematician,
so maybe he knew something that we don't. And Fibonacci was a transformative
genius, he did
many transformations. He created a new
world and we actually live in the new
world
that he created. Let me show you what he
did, but first let me clear this board.
Around 1200 A.D, Fibonacci publishes
a great book called Liber
Abacci.
This word means the abacus,
the abacus is the instrument with
strings and beads
which is used in calculation.
Maybe you can identify this from the
word
Library
which means book. So many people think
this means
the book of abacus or book of
calculation,
and if you go to Wikipedia, even
Wikipedia says
'Liber Abacci' means the 'Book of
Calculation'.
But the wordLiber
also appears
in this word Liberate or Free.
Fibonacci was using this word to say
'Free the
Abacus'.
What does it mean? At that time in
Europe, all the people were still
using roman numerals and the abacus and
they were doing
all the calculations with abacus.
Fibonacci, after studying the Hindu
calculation system, wanted to
change Europe, he wanted people to get
rid of the abacus
and start following the Hindu
calculation system
of using addition, subtraction,
multiplication and division. This is
called
arithmetic.
So think about this, how do we do
calculations today? So
if i have to say, what is 15 + 16
how do i instantly know it's 31?
How do i know the answer is 31? 800 years
ago
before the time of Fibonacci, if you went
to Europe and if you said what is
15 + 16, they would need an abacus
and they would start working with the
beads to come up with this number.
Without using an abacus why am i able to
do this
using a marker and a board or even
better,
I knew the answer in my mind. So who
invented this modern arithmetic?
it was Brahmagupta, it was a great
another
great Hindu mathematician who
lived around 600 A.D,
so this is about 1400 years ago.
And the modern arithmetic, the addition,
subtraction, multiplication, division
and all these numbers with the place
value and doing all these complicated
maths,
was invented by Brahmagupta. Today
we follow the system around the world,
but it was originally invented by
another Hindu mathematician.
And this method fascinated
Fibonacci so much, he wanted
the entire Europe to learn
this type of calculation. He wanted
people to free the abacus and stop
using roman numerals and start using the
Hindu arithmetic all over Europe. This
was the purpose
of Liber Abacci.
Now, the Liber Abacci has many chapters
which talks about various methods of
Hindu calculation, this is why he called
this Modus Indorum and the actual
Fibonacci numbers
is only a small part of this book.
So what happens after Fibonacci
publishes this book in 1200 A.D?
I told you Fibonacci was a
transformative
genius, he revolutionizes
trade, commerce, business, banking,
weights and measures, and he completely
alters the system
in Europe. Everybody in Europe was
picking up this new method of
calculation.
Now think about this, before this book
got published
if you go to a bank and if you give them
50 bucks and if you ask for some change,
everybody would literally pull out an
abacus
and they had to do the calculation to
see how much
they have to give you. And Fibonacci
changes this dramatically, the entire
Europe gets revolutionized by this
Hindu system. Now, how successful
was Fibonacci in liberating the abacus?
If you read history, it's very
interesting, because in the city of
Florence in Italy, the bookkeepers
actually passed a law saying
that they should only use roman numerals
and abacus
and not use the new Hindu system.
And of course it did not work, because
everybody switched to the
Hindu mathematical system and the
bookkeepers
went out of business. So Fibonacci
was amazingly successful in introducing
the method of the Indians to Europe. In
fact,
some even believe it's because of this
new
method, business became so big in Europe
and they were able to accumulate so much
wealth,
they were able to conquer the entire
world
in a few centuries. So at this point,
there should be no doubt
in your mind that the Fibonacci number
originally
came from ancient India and
it was discovered by Hindu
mathematicians,
but there is another question:
Did Pingala discover the Fibonacci
number
by himself? Or did he get it
from an even more ancient Hindu source?
Maybe we can take a look at this in the
next video.
I hope you guys like this video, I am
Praveen Mohan, thanks a lot for watching,
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and i will talk to you soon. Bye!
 
