Give and Take

What can I give to the society?
I can give theory on numbers. Let us say it will earn me $x.

What is it that I want to learn?

1. I want to learn caricature and cartooning from the best( Disney Level teacher).  Mentally I think I will have to spend $0.6x.
2. I want to learn chess from Indian Grandmasters. Mentally I think I will have to spend $0.4x.

So what I can teach and what I want to learn are balanced. Total earning potential = Total desires in learning.

Many of you may want to enquire, whether I do not want to learn carnatic in violin or electric guitar. My interests have subdued in music learning. Currently caricatures, cartoons and chess are high in interests.

( I beat Stockfish 2 AI level in lichess.org. Though I have a feeling that I can reach Stockfish 4 AI Level).

Litti Chokha

Litti Chokha is a famous dish in Ranchi.
Litti is wheat flour balls filled with Sattu(secret recipe containing chana dal and other ingredients)  and fried in desi ghee after heating the balls up in coal stove. First the balls are made. Then heated up. Then fried in ghee.
Chokha is Aloo bhaji with mild spices.
The combination is excellent and well balanced too for an Indian.
I remember there is a shop in Vikas Marg, Delhi selling Litti.
Two Litttis and Chokha will serve as a nice lunch during winters. If served with mildly spiced buttermilk; this combination may go well with foreigners too.

#PythaShastri growth blog post

Growth is an important point to ponder for humanity. Particularly for Indians as we are the second most populous country in the world and we are going to be the most populous in a few years.
Many of the points that I write below are not mathematical points but at the most pseudo-mathematical.
The growth in terms of e series is different and involves trigonometric functions and are not pure number theory. It is also alien to Indian mindset.
Ramanujan gave us growth series analysis in log terms. Ramanujan-Soldner constant and Ramanujan -Landau constant are factors which give meaning to the log series.
#PythaShastri has given growth analysis in terms of rational numbers, their growth and their growth in terms of squares and square roots too. My last two posts in this blog and also a blog post in Power of your company blog is about that.
The e series and log series are certainly not Indian patents. (I personally have a Russian mindset and do not like patents though).
Now I pose this question to Indians. Do you think growth is important as a theory? (Not practical growth. We are already experts here !!)
If you answer yes; Does a person in R & D got a role?
If you answer yes. Does such a person needs food for thought (training or posting) for growth?
Yes. But #PythaShastri is not the right person is one answer.
No. Food for thought is not required is another answer.
I like the first answer. I just hate the second answer. Food for thought is not required. Food itself is not required.
This is not the right forum. Keeping people waiting for the right forum. We are Salem in SAIL. We have a right to demand a forum I think.

#PythaShastri another approximate formula

#PythaShastri has discovered another approximate formula. I was very close to square roots of numbers and I tried to use my earlier method to square roots. The results are interesting and gives an approximate pattern and is accurate at higher numbers.
n - (((n+1)^0.5)((n-1)^0.5)) is approximately 1/(2n).

#PythaShastri approximate formula

#PythaShastri approximate formula is
(n^2)/((n+1)^2) - ((n-1)^2)/(n^2) is approximately 2/((n+1)^2).
This is a thumb rule sort of equation. The higher the value of n, better is the approximation.
This gives a sense of growth of squares. The percentage growth of squares is approximately 2 by the current square.
This has practical thumb rule application in areas where squares of numbers are involved. Perhaps population, rumour growth, fear spreading calculations etc.

#PythaShastri Methods

#PythaShastri demonstrated abilities in mathematical expressions. There were expressions on π, e, γ and φ (pentagon demonstration). I thought this was enough to get me fame and recognition. But nothing arrived. Then, #PythaShastri moved ahead.
The other day I saw in Wikipedia articles on Taylor and McLaurin. They are Scottish mathematicians. They are genius of unfathomable level. Too good to be true. They have done God level work. Indian educational curriculum owes a hell lot to these gentlemen. Our education system is incomplete without considering their contribution.
#PythaShastri realised that his work is that of Taylor and McLaurin. Though an original thought; nevertheless the fact cannot be denied that series expressions are of Taylor and McLaurin origin.
I then thought let me express sines, cosines and log in terms of my discoveries.
My expressions worked and gave some results.
#PythaShastri feels he is far from over. Only now he has entered the real mathematical methods zone. Give me a chance and I shall prove my ability.

I feel like expressing "Now", "இப்போது","अभी". It is tough to explain what I mean. But this is the core, I feel we lack in mathematics.

Anyway, here are the results:-

#PythaShastri 4 pi expressions

#PythaShastri 4 pi expressions.
They are fast. They are with combinations. And they are: