Mathematical Mahabharata

 The children between the age of five and seven are true word-lovers. They show a predisposition toward such a study. Their minds are undeveloped hence cannot yet grasp any simple idea with disagreement.

At the age of eight, I was made to learn Sanskrit and Vedic mathematics with the highest quality of learning and a logical approach to the solutions. The concept of Gurukulam or alternate school where the parents submit their kids to the institute to make them the most excellent scholar in Philosophy is the age-old practice. I was fortunate I had to go through that at the early stages of my life, which doctrine the discipline of reading, analysing, and debating over the philosophical concepts that are strenuous and are far beyond the understanding level of any other kid in the schools of Modern education system. One should visit these schools at least once in their lifetime to understand the actual meaning of education and teacher. It's not a marvel that you might get to see a kid of eight or nine-year-old reciting the formulae of calculus and trigonometry along with the chapters of Bhagavad-Gita in one go.

When my teacher told me, "Bhagavad-Gita – "The song of God," I was the most confused person in the world!! I wondered, aren't we supposed to sing for god, why is god himself singing for us? Then I consoled myself saying, if a god is singing for us, then I should learn this. As the reading and learning followed, I came across the 16th chapter named Daivasura sampadvibhaga-Yoga," which means "The Yoga of the Distinction Between Binding and Liberating Conditions," Way beyond understanding capabilities for a 10-year-old boy.

The 6th verse of that chapter had the following two lines.

 

द्वौ भूतसर्गौ लोकेऽस्मिन्दैव आसुर एव च |

दैवो विस्तरश: प्रोक्त आसुरं पार्थ मे शृणु || 6||

Translation:

There are two kinds of beings in this world 

Those who are endowed with a divine nature and those who are possessing a demoniac nature. I have described the divine qualities in detail, Oh Arjun. Now hear from me about the demoniac life.

I wasn't sure what Lord Krishna was conveying, but I was positive that there is some coded information that I will have to decode one day!

Number theory is one of the vast fields of mathematics, one can go on to teach and learn this concept for decades, but still, there will be a topic of sea left to learn. The first and the foremost of all the subjects taught under quantitative aptitude is Number theory due to its vast nature, and the concepts under this topic work as fundamental to the progressive ideas.

I was standing in front of quick-witted engineering students, I could sense all the students were eagerly waiting for my instruction, "Drop the pen and stretch back."  Whenever I said these words, students knew that I would be giving them a piece of brand-new information about the topic of the day. 

"Average of four prime numbers is 22.75, then which prime is compulsorily one of them?" 

An item from the Mathematics topic Averages. The whole class was trying to achieve the solution, but none came up with the correct answer. The class was furious as they could not solve it. All the students looked at me for the solution, and I knew they should think like Lord Krishna to solve the problem. I narrated them a story in a few minutes, which helped them in solving the problem. Even though Lord Krishna created the idea of the concept, it is my guru Gayathri ma'am who made me understand the value of numbers through dance.

Thatti mettu adavu is one the prime parts of all the dances of Bharata Natyam, without which any choreography is incomplete. It's a pure mathematical based rhythmic movement whose calculations are fixed by the teacher while composing the song or while choreographing the dance for it. This step requires a dancer to stamp the foot on the floor. And a soft movement of touching the floor with feet and dropping the feet. Every song is set to different thalam (Beats); one can neither exceed the predefined beats nor fall short of beats while executing this Tatti mettu adavu.  Traditionally a line of the song is thrice for a Bharta Natyam performance, and the dancer expresses the meaning of the lyrics through hand gestures and facial expressions for the first and second time. The third time additional footwork using Tatti mettu adavu is done, which is the most challenging part of learning for most of the students as one has to execute the movement of leg and hands in synchronization to a particular thalam. 

I was fortunate enough to learn a Bhajan Set to Khandachapu thalam and is in Brundavani Sarag rāgam. Khandachapu literally translates to "The rhythm of five beats." The word Gati means speed, and since the beats decided the rate of the song, the beats are called Gati in Carnatic music. Following is the list of Gati with their mathematical equivalents in terms of beats.

Gati

Phenetic representations of beats

Mathematical sum

While learning the Bhajan Which was set Khandachapu Thalam, the multiples of five was in my mind, especially during Thatti Mettu movements. I went wrong in executing specific places as I was counting 1 2 3 4 5. Even though it was matching the song, it didn't help me in performing the steps without any mistakes. My teacher stopped me halfway and asked me, ", What are you counting?" To which when I replied 12345. She said count 12 123 as the Shollu kattu goes

Tha ka, Tha ki Ta. She said at the end," Adding 2 with 3 will give you 5." 

(As we watched and learnt the movement from our Guru)

Even and odd gives you odd. She took me further closer to the solution, and I realized what she meant by that. To get an odd number 5 as the total using a combination of two different digits, one must add an odd number to one even number. 

I asked the students, "what did we learn from the above story?"

Students replied with the following cases as their answers:

The operations of odd and even numbers

Odd + Odd = Even

Even + Even = Even

Odd + Even = Odd

Even + Odd = Odd

"Average of four prime numbers is 22.75, then which prime is compulsorily one of them?"

Solution:

Let w, x, y, and z be the prime numbers.

If w+x+y+z/4  = 22.75 

w+x+y+z = 22.75 *4 = 91  (Cross multiplication)

The number on the right-hand side is 91, which is odd. All the prime numbers in the world are odd except the number 2. Hence to get odd on the right-hand side, one should add one even number to any number of odd numbers to obtain the result. Hence the correct answer is 2.

I quoted what Krishna said to Arjuna in the 6th verse of chapter 16th. As I explained the duality of the number 2. The number 2 is divine and demonic in nature as it is prime and also even at the same time.