Summation theory - not by German Mathematicians, Pythagoras theorem - not by Pythagoras

Did you have an interesting climax in my last blog?? Just what all mega serials follow for weekends:-) :-)

So, this blog is going to let you know some unrevealed truth about one of our most favorite/disgusting subject of educational system. Yes, it is - "MATHEMATICS'. Many of us love 'MATHS' (as it is called), while most of us hate it. Lovers because it loves them back and same is with the haters as well :-).

Jokes apart, the topic clearly states the truth that I am trying to emphasis. The 'Summation theory' and 'Pythagoras theorem' alone are not involved in this dispute. Rather all the concepts, theories, formulas comprising 'Maths' and 'AstroPhysics'  are to be taken into account.

For your information(FYI), some significant theories and topics which are familiar are listed below :

Summation theory

Pythagoras theorem

Fourier transformation

Algebra

Trigonometry

Square/Cube/N roots

Differential Calculus

Geometry and many more..

Even if 'Maths' and 'Physics' are not your favorite subjects, what if I say that the authors of the above list as we know, are not the actual owners of their masterpiece, and that they have copied the concepts. Dont you feel shocked? When we feel that these people have had extraordinary brilliance, what about the proprietors.

Who could they be?

Yes, they are OUR people. Our own 'Bhaskaracharya' , 'Aryabhata', 'Bhramagupta','Baudhayana'  and many more. They have written the concepts and formulas in the form of verses, and when we realize or look into them in detail, we can find the theory and its proof.

For our better understanding lets us take 'Summation theory'.

Summation theory
For those who are not aware of it,

where Summation is the operation of adding a sequence of numbers. This theory states that if numbers are added sequentially from left to right, any intermediate result is a running total of the summation(definition can be ignored :-))

For example, if we want to find sum of numbers from 1 to 5, how do we do that?

1 + 2 + 3 + 4 + 5 = 15. This is a simple summation. What if the number is big. For example, say from 1 to 55,                                                                                  

                                                                  

                                                                   =   1540

This is a sample to make you understand what this Summation theory is. This formula is taught to us in our school. A new symbol to represent the concept of Summation with positioning of limits and such things makes it look so professional. 

But as 'blamed', this concept has been copied from one of our greatest minds 'Bhaskaracharya'. In one of his top books 'Siddhanta Siromani' written long long time back he has created the formula for Summation of N numbers. How?

                                                                          

"saikapadhdhna padhaarthamithaikaadhyankayuthihi kalu sankalithaakya"

This verse in Sanskrit tells us the definition of Summation theory as carved today. On splitting this verse into micro level one can find the definition, which says, 

"when a padham (a number/quantity),  which is incremented by one (saikapadha) and split into 2 halves (padhaartham) and multiplied by the Padham (same number) gives a quantity that is equal to the sequential addition or summation of all the  numbers that lies below the padham starting from 1 (eka anka yuthihi kalu sankalithaakya)" 

Pythagoras theorum

Lets have a glimpse on it. The definition stated for this theorem is as follows..

In any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).The theorem can be written as an equation relating the lengths of the sides a, b and c, often called the Pythagorean equation:

where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides.

This concept was formulated by the same legend 'Bhaskaracharya' in the same book.He assumed a Garuda (Type of vulture) sitting on a tree with a straight trunk, aiming to catch a snake at a certain distance from the tree making a triangle like illusion as example and formulated this concept.  

Pythagoras while traveling across the world in quest of knowledge came across this master mind in India. He acquired these concepts from him and projected to this world as his theorem with his own definition and proof. Here's what 'Bhaskaracharya' left for us that explains the whole Pythagoras theorem.

"dirghasyaksanaya rajjuh parsvamani, tiryadam mani, cha yatprthagbhute kurutastadubhayan karoti"

Reason for us not following our ancestors

            If our ancestors are the fathers of Maths and Astro Physics why are we not having their hand written books and their way of teaching in our educational system? In spite of knowing the truth we are forced to study the refined, sophisticated version of the same concepts, copied by the modern inventors. Why? The reason is simple. In this modern world nobody is accepting things without equational proof. No matter how clear the explanation is, how simple the example(all real time) is, how understandable it is, there was lack of evaluational proof  i.e Left-hand-side = Right-hand-side. 

              This mechanism is accepted as a theorem by our modern world. They just want simple notations. Our ancient vedic mathematicians also had equational proofs for all the theories but they were taught to their students in a different manner.

Not to be denied, for the mega mind who found out the value of 'pi' to be 3.1416 (accurate to four decimal places) with derivational proof in the past, it is not a big deal to write equations and proofs. But those legends preferred 'Maths' to be simple with real time examples such as this Garuda and snake. All the theories were involving simple real time examples that made the modern mathematicians feel unsure if the theory was perfect or not. So they created new notations, equations and what not, and carved the equational proof and that is what is followed till date. 

        Nevertheless, we cant deny that almost all of the concepts were 'borrowed and renovated'.

Thats it! Hope you guys are now feeling proud to know that we are from the country(India) where the "Masters of the universe" were born:-) 

Wait for the next blog to get to know about the "Massive energy stations of the past". Guess what I am referring to.. till then take care!!