How Fibonacci number series originated in Ancient India

[FBInCIAnNSATerroristSlayer]

Fibonacci Sequence MUST BE renamed "Pingali/Virahanka" Sequence.

Fibonacci himself admitted that "he merely translated Indian mathematics".

Western white christians NOT ONLY STOLE land and wealth, they also stole
knowledge of Non-Whites and claimed as their own "to establish white
supremacy" in order to lord over non-whites forever.

Dumb Non-whites think Whites are civilized because some whites criticize
racism BUT IN REALITY "Whites have done NOTHING" in terms of "returning
the stolen land, stolen wealth, paying reparations to blacks, browns and
yellows AND giving credit to non-whites' inventions and discoveries"



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http://guruprasad.net/posts/fibonacci-number-series-originated-ancient-india/

How Fibonacci number series originated in Ancient India

Almost 2 decades ago, I was introduced to the fascinating concept called
Fibonacci series, by the book “Da Vinci Code” authored by Dan Brown,
which was highly circulated among friends & the most talked about book
in our college back then.

Thanks to the book, Fibonacci series & its related concepts like Golden
Ratio, Phi, Combinatorics, etc had evoked a sense of scientific temper &
analytical thought processes.

In the subsequent semesters, as our professors taught us lessons on
Fibonacci & its applications in real world, my respect for Leonardo
Fibonacci, (The Italian Mathematician who’s credited for the
conceptualization of the numerical series in 13th century AD) had simply
skyrocketed. For the next whole decade, I was in awe of the Italian
Mathematicians & felt greatly indebted to him for his contribution.

Fast forward to 2015. While browsing through some books of a 20th
century Indian Philosopher, I came across an excerpt of his speech in
which he made an outright claim that Fibonacci series had actually
originated in India, more than 2500+ years ago!! That set my pulse
racing, and it was time to go deep into this to find out the truth so
that due credit could be given to those who really deserved it. And the
results were enthralling to say the least. Let me take this opportunity
to concisely narrate the story of this wonderful series & the real
scholars behind it.

Way back in the 2nd century BCE, when Sanskrit & Hinduism were at their
peak in the Indian sub-continent, Hindus were accumulating knowledge
like never before. However, what’s the point in accumulating knowledge
without propagating it further? That’s where Sanskrit played a major
role. Thanks to the flexible characteristic of the language, it was the
ideal language to compose poetry by imbibing these learning into poems &
propagating them through oral means.

Hence, the art of poetry in Sanskrit, was not just a matter of
entertainment, but actually a methodology to exchange ideas & spread
knowledge. Almost all knowledge, be it scientific or medical or
philosophical or spiritual or astronomical or astrological, were all in
the form of poetry. In fact, some of the mega-epics of India, like the
Mahabharata, Ramayana, and the philosophical works like Bhagavad Gita,
were all poems. In fact, Mahabharata, in its original poetry form, by
itself, has more than 1 lakh shlokas.

With this understanding of how & why Sanskrit Poetry was the ideal
medium for knowledge, here comes the next challenge. How to compose the
poems efficiently so that it can be relatively easier for the scholars
to remember & recite them?

That’s where the concept of “Sanskrit Prosody” comes into picture. This
is basically a methodology based on rhythms & arrangement of tones. Not
only is it a method, but actually a vast field of study where natural
rhythms are determined so as to form a framework for poetry which would
be very pleasing to the ears. The poems which are then composed based on
this framework, would abide by the laws of nature, hence making the
poems sound naturally pleasant, thereby enhancing the probability of it
being remembered for a long time in the human mind, with minimal effort.

This “pleasant” effect in Sanskrit is called “Chanda” which is based on
the root word “Chand” which means “pleasing”. Hence, this poetry
framework, whose aim was to produce pleasant poems, was called “Chandas”
in Sanskrit or “Chandassu” in Kannada or Telugu. Since it is like a tool
which is to be utilized for fields like poetry, it was considered a
sutra/shastra, and hence this methodology was also called “Chandas
Sutra” or “Chandas Shastra”.

Now, you might be wondering as to how we started the discussion with
something as mathematical as Fibonacci series, but are touching upon
topics like poems & Sanskrit Sutras. Well, that’s the beauty of ancient
Indian wisdom. What we think is art, is actually beyond that. In ancient
India, poems were not merely art forms produced out of creative juices,
but had to inculcate highly sophisticated Mathematical concepts in order
to pass the test of Sanskrit Shlokas. Chanda Shastra was one such
mathematical concept which were widely used by the poets.

In Chanda Shastra, everything finally boils down to 2 syllables: Short
syllable which need 1 beat (Laghu) and Long syllable which require 2
beats (Guru). Musicians like Tabla players also use the same concept,
where they call Short syllable as “Dhin” & Long syllable as “Dha”.


Now, let’s try to step into the shoes of a poet to understand the
significance of this Chanda Shastra. Since every poet begins composing
his poem by fixing the total number of beats per line/shloka, his
creativity can get drastically constricted because his content in each
line must fulfill the criteria of the total beats per line. Hence, there
is a need for the poet, well in advance, to be aware of how he can
arrange the Laghus & Gurus in each shloka, and how many such
combinations are possible for each shloka.

Let’s consider a simple hypothetical case of just 2 beats per shloka.
With this assumption, how many combinations of Laghus (short syllable)
& Gurus (long syllables) can be formed?
Simple. Since there are only 2 beats, it can either be filled with 2
Laghus or 1 Guru. Means there are 2 combinations.

Next, what if there are 3 beats? It can have any of the following
combinations:
1) 1 Laghu & 1 Guru
2) 1 Guru & 1 Laghu
3) All the 3 Laghus

So, it means, we can have 3 combinations. i.e There are 3 ways of
arranging short & long syllables if we are asked to compose a shloka
containing 3 beats.

We can go on with these calculations and determine that when we have 4
beats, we can have 5 combinations. When we have 5 beats, we can have 9
combinations. When we have 6 beats, we can have 13 combinations. When we
have 7 beats, we can have 21 combinations. For 8 beats, we can have 34
combinations. And so on.

Summarizing the above paragraph, we can have 1, 2, 3, 5, 8, 13, 21, 34
(….. upto infinity) combinations.
If we closely observe the above pattern, we note that it is actually
nothing but the series which we today popular refer to as Fibonacci
series. This is what the whole subject of Chanda Shastra is based upon.

And that takes us to the actual topic now. What we call as Chanda
Shastra, was pioneered by a Saint-Scholar (Rishi) named Pingala in the
2nd century BC. (Although recent archeological evidences suggest that it
was 4th century BC).

In fact, not only did Pingala conceptualize the series (what we call as
Fibonacci series today) as part of Chanda Shastra, but even extended it
to the concept of a pyramid of stacked numbers which we call as
“Pascal’s Triangle” today. However, during Pingala’s era, since Mount
Meru was commonly used as a reference to the centre of Hindu
civilization, he had called his stack of numbers as “Maatra Meru” which
he had claimed converges towards the Golden Mean.

An excerpt from a well researched book titled The “Venus Blueprint:
Uncovering the Ancient Science of Sacred Spaces” has illustrated it very
well, and an excerpt of it (Page 50 to be precise) is presented below:

Reference:
https://books.google.co.in/books?id=OrdrXuS15XQC&pg=PA50#v=onepage&q&f=false

As we can see, Fibonacci Series & its extension i.e Pascal’s Triangle,
were already described by Pingala 2500 years ago as part of Chandas
Shastra, with reference to Matra-Meru, & the concept has been used by
Sanskrit Poets for 2000+ years.

Not only by Sanskrit poets, but by Indian classical musicians (including
Hindustani & Carnatic forms) as well.

For example, here is an interesting demonstration (video embedded under
this paragraph) of rhythms in Konnakol form, which is a part of Carnatic
music, and one can see how it is in accordance with Pingala’s Chandas
Shastra, which we call as Fibonacci Series now.

If the above embedded video is not working on your PC/Device, you can
watch it directly on YouTube by clicking the following link:
https://www.youtube.com/watch?v=Zc7WMbVW-3s

For centuries, these number series have been in use especially by Indian
poets & classical musicians, and there have been detailed commentaries
of Pingala Chandas Shastra made by ancient Indian scholars as well for
their respective fields. For instance, in the 5th century AD, the Indian
Astronomer-Mathematician Varahamihira had used the same sequence in his
works related to Binomial Coefficients. This is in fact well
acknowledged by the Mathematical community now and is nowadays being
cited in their research works as well.

Following is an excerpt from a paper published at “Scientific Research
Publishing” where this historical fact is being acknowledged & credit is
given the above mentioned Ancient Indian Scholars.

Reference:
https://file.scirp.org/pdf/AM_2015061016154083.pdf

While Pingala & Varahamihira had used the number series for their
respective fields like Sanskrit Prosody & Astronomy, one of the most
comprehensive commentary on it applying it to various other fields, was
later done by a Hindu Jain Scholar named Acharya Hemachandra in the 12th
century AD.

Documentary evidences show that Acharya Hemachandra had compiled his
treatise in 1150 AD, whereas Leonardo Fibonacci had presented his thesis
only in 1202 AD, which looked identical to that of the commentary made
by Hemachandra. Hence, this proves that even in the form of a treatise,
the number series presented by the Indian Scholar Hemachandra, had
preceded that of Leonardo Fibonacci by more than half a century!!

Thanks to the awareness spread by Indian scientists worldwide about this
fact & evidence, almost all the Mathematicians, and the Scientific
Community in general, have started acknowledging this, and are giving
credit where it is due, by mentioning Fibonacci numbers as
“Hemachandra-Fibonacci numbers”, which is the first step in the
awareness process, with the hope that it will some day in future be
referred to as “Pingala-Hemachandra numbers”.

Following is an excerpt from a Quantum Mechanics book in which the
author has given due credit to Ancient Indian Scholars & has referred to
the series as Hemachandra-Fibonacci numbers.

Reference:
https://books.google.co.in/books?id=toIRDQAAQBAJ&pg=SA4-PA2#v=onepage&q&f=false

Meanwhile, one such Mathematician from Indian descent, who is putting
immense efforts into spreading this awareness about the origins of
Fibonacci series in India, is Manjul Bhargava, who is currently a
Professor of Mathematics at Princeton University. On a regular basis, he
conducts workshops & seminars in which he shares insights into these
concepts & makes them interesting by relating them with real world
applications, including poetry & music.


If you can spare a few mins, I strongly suggest you to watch one of his
recent talks (video embedded below this paragraph) in which Manjul
Bhargava, in his signature style, explains how Hemachandra numbers
(Fibonacci numbers) are being an integral part of various fields like
nature, poetry, art & music:

If the above embedded video is not working on your PC/Device, you can
watch it directly on YouTube by clicking the following link:
https://www.youtube.com/watch?v=siFBqH-LaQQ

As more professors like Manjul Bhargava continue to rise up to the
occasion to spread further awareness about this concept and its origins,
the rest of the world will not be able to ignore it anymore, and start
acknowledging our ancient Rishis who deserve real credit. Also, thanks
to the advent of internet technologies & social media, more Indians are
also becoming aware of their own glorious history, helping in
inculcating national pride within themselves, which our previous Govts
had carefully chosen to ignore, for reasons best known to them.


With all these evidences & explanations, we can now see how the
fascinating number series, which we call as Fibonacci series today, had
originated in India and has been in use for centuries, thanks to the
foundation laid by Pingala 2500 years ago, and the legacy strengthened
by Hemachandra more than 1000 years ago.

Now, the least we can do, is to acknowledge the roles of our ancient
Indian scholars & Rishis, and start giving them due credit, by referring
to the Fibonacci series as “Pingala-Hemachandra” series. The global
scientific community has already started the process (by including
Hemachandra’s name). It is now the turn of Indian academicians &
educationalists to imbibe these into school textbooks as well, so that
future generations can be proud of our Rishis in particular & our
ancient wisdom in general.

[William]

On Monday, May 18, 2020 at 3:11:36 AM UTC-3, FBInCIAnNSATerroristSlayer wrote:
> Fibonacci Sequence MUST BE renamed "Pingali/Virahanka" Sequence.

Indeed, as every other name in mathematics accurately describes provenance.

[FromTheRafters]

William expressed precisely :

https://en.wikipedia.org/wiki/Stigler%27s_law_of_eponymy