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 atcell 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. Nowyou 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 thescales, 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 8^{th} 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 theHindu 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 word Liber 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.