About Chess

I have done two things to try and beat the tab chess app.
1. Bought a kindle book on chess.
2. Working out with Chess King Learn app.

My rating is falling. Facing tough exercises.

My rating has climbed up now.

The Golden Ratio

The expression for root 5 is

The expression for phi the golden ratio is 

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:

My dreams

My dreams are :-
1. Get formal education in higher mathematics.
2. To develop software for some of my solutions.
Being in research I can dream in research fields. Earlier I was in IT.

BrahMos Missile

The BrahMos (designated PJ-10) is a medium-range ramjet supersonic cruise missile that can be launched from submarine, ships, aircraft, or land. It is the fastest cruise missile in the world. It is a joint venture between the Russian Federation's NPO Mashinostroyeniya and India's Defence Research and Development Organisation (DRDO) who together have formed BrahMos Aerospace. It is based on the Russian P-800 Oniks cruise missile and other similar sea-skimming Russian cruise missile technology. The name BrahMos is a portmanteau formed from the names of two rivers, the Brahmaputra of India and the Moskva of Russia.

It is the world's fastest anti-ship cruise missile in operation. The missile travels at speeds of Mach 2.8 to 3.0,which is being upgraded to Mach 5.0. The land-launched and ship-launched versions are already in service, with the air and submarine-launched versions currently in the testing phase. An air-launched variant of BrahMos appeared in 2012. A hypersonic version of the missile, BrahMos-II, is also presently under development with a speed of Mach 7-8 to boost aerial fast strike capability. It is expected to be ready for testing by 2020.

India wanted the BrahMos to be based on a mid range cruise missile like the P-700 Granit. Its propulsion is based on the Russian missile, and missile guidance has been developed by BrahMos Aerospace. The missile is expected to reach a total order US$13 billion.

In 2016, as India became a member of the Missile Technology Control Regime (MTCR), India and Russia are now planning to jointly develop a new generation of Brahmos missiles with 600 km-plus range and an ability to hit protected targets with pinpoint accuracy.

#PythaShastri and Euler equation

Remember #PythaShastri right triangle with x and x squared as sides.
Now, product of 1/(prime squared) is according to me is 4/10.
Let's take 40.
Add 1 on both sides.
(1 + product of primes)/(product of primes) = 1.
1 = 41.
Add 41 to x squared + x.
What do we get?
x squared + x + 41.
And above is the Euler prime generating polynomial.

#PythaShastri and Euler identity

#PythaShastri and Euler identity

Symbolab app installed

I have installed symbolab app in my Samsung mobile.
Here are the snapshots:

Basel Problem 2

#PythaShastri Finishes. Sigma and Integral equivalence.

Basel Problem

Newer Areas

Some newer areas of thoughts have been shared by me on the internet via blogspot which is a Google product.
These are:
1. Puzzles to improve wisdom of finances.
2. Infinite series statements based on higher fibonacci confidence.
I can involve in this realm for a while. It's a greenfield investment opportunities.

The greatest genius

It isn't about IQ. It is possibly imagination and calculations most efficiently used. I thought it must be Leonardo Da Vinci. But I was not sure. Maybe it was Einstein.

Today it is clear. It is Leonardo Da Vinci who is the greatest genius.

Something Worthwhile

Could you have crossed that line without a care for the self being burnt? No, never.
The hell is within. And they rise. It is magnanimity that rules the soul. And not otherwise. However dependence on what not is arbitrary and without merit.
They say people gossip. Really !! That matters, so do I for myself. Any chance however to help the helpless is a matter of deep concern. To me. And my other part.
How can somebody be so lazy? Waiting for the ripe banana to fall may be a solution but not a problem. Take it this way. That Way. Any Way. I wish to write that when pigeons fly their aim is to reach the destination. Her interest is certainly not in laying eggs for the he pigeon. However when things go wild as they seem every time; Only one thing helps. A true self.
Therefore it will be more appropriate to consider a true self as being conquered within. To say the least.

Chess and tick mark law

Tick mark is the angle formed by pieces.
More the area covered by tick marks, more is your chance to win.
How is this?

Shades and Lines

#PythaShastri another two hands solution

#PythaShastri another two hand solution is as below

#PythaShastri two hands pi formula

#PythaShastri two hands pi formula is working. Here it is:

Well, (2n(2n-1) is left-hand and (3n(3n-1)(3n-2)) is the right hand. And it results in pi expansions as per Wolfram.

#PythaShastri eyes 3 and squared terms for pi and e

#PythaShastri eyes 3 and squared terms for pi and e.
And pi and e terms comes out with irrational, rational and other terms.

My desires

The other day, I was thinking of what are my desires? What do I expect more from life? I have got a lot. I have given also. For example the factor like n! by (n!)^n explanation based on extroverted theory is a small contribution from my side. It is the foundation of the fastest pi series.
What are my desires? Two things.
1. Complete and extensive number theories knowledge.
2. Lou Darvas, Ken Hultgren, Tom Richmond levels of skills in cartoons and caricatures.
That's all.
I shall make these desires fulfilled in this lifetime. But it is possibly not possible by self coaching. I do self coaching. And that is the only way with my reach.
I expect the society to fulfil these, but in India there is only discouragement. It pains.

The Sun rises . . . . and sets, eveyday

The Sun rises . . . . and sets, everyday. It is about another aspect of my life. It is quite fearful. The Sun rises . . . . and sets, everyday is about mathematical constants.

Why did I write about Sun? Because of repetitions and being infinite. Similar to mathematical constants.

There is so much of fight over God. Many imagine God to be sitting above clouds and deciding on heaven and hell. Having faith in God, presumably gives direction to men and keeps them away from doing bad things.

To me repetitions and infinity are much more closer than God. Why don't people repeat things steadfastly with strength like Sun and do things? I wonder !!

I feel repetitions and strength and motivation inspired from Sun should be considered God. It will give courage, hope, sincerity. It will improve India. It will develop personality.

I have come to a dead end with respect to constants. I do not know how to go further. In India there are courses and procedures for admission to courses.

I wish I had somebody like Prof. Hardy who guided Ramanujan and offered him scholarship to study in Cambridge. Wow !! How kind of Prof. Hardy !!

Shades and Lines

Shades and Lines. It is about one aspect of my life. It is quite dear to me. Shades and lines is about drawing notebook and pencils.
It can be a bread earner. It is a hobby. It can amplify what you want to communicate by many times. It gives peace and sense of fulfillment.
But today the technology has changed. Software rules high in shades and lines. I am all for technology.Times have changed and technology has arrived. I am also in favor of twisting photographs and making caricatures. The effect can be mind blowing. But I need training in Adobe illustrator and other important software to be able to do something.
But one thing in favor of pencil shades and lines is that it has a distinct flavor. I guess my flavor is close to that of Madan. And a little R K Laxman. Anyway, others need to say.
There is a market for flavor. There is still a market for pencils. But one needs to be aligned with editorial team's thought process, too. This is very important.
Nowadays, I miss seeing cartoons. Satish Acharya cartoons, I see more frequently than others. I miss Ajit Ninan Mathew.
I use Google Images to catch up with cartoons.
Have a nice day !!

Animated cartoon

I have made a animated picture from my cartoon.
I was inspired by one of the fellow bloggers. And thought, let me try.

#PythaShastri more expressions on e and π

The above are some more expressions on e and π.
e is an important constant, which occurs in nature. Euler worked a lot and did a lot on e.
Another expression of π is also pasted. This expression reaches to π quite efficiently and can be used in some graduation and post-graduation courses. Any help needed on inclusion in curricula will be obliged.
How do I make expressions? There are certain numbers and theories in me. There is a pattern in these. These patterns, I try to explain in mathematical expressions.  As an example (-1) ^ (n+1) is actually talking of odds and evens. For when n is odd + sign is returned. And when n is even - sign is returned. So (-1)^(n+1) talks of odds and evens.

Meaning of my life

The life of an individual is bound by two things. One is his own principles. The system prevalent in his society. By society, I mean the place he lives;the friends and relatives; and maybe other factors.
Earlier, I tried to lead an accountable life. And I thought accountable life is parmo dharma. But people around did not seem to care for accounting.
So, I changed the meaning of my life. It is no longer accounting. But conscience and quality are the two words driving my life.
About society, I hate helplessness. And I expect society to follow successful models of working than to be a society that sets examples. I feel India should follow China or US rather than spending energy on making India great.

These days . . .

It was impossible to go ahead further on mathematics series. I know and can explain the most famous constants of e, pi, gamma and phi. But my pi expressions are not the fastest. I wanted to read books on higher number theories. But these are tough. Therefore, I have stopped mathematics research.
Cartooning and caricatures are possible only to a certain extent. Linear progress as a function of linear time is not possible. Therefore, I have restricted myself in cartoons and caricatures too.
I am working on chess and now my elo rating is 1520. Here is the snapshots.

Working and improving on chess is more fruitful.
1520 is good for clubs. But not possibly good enough to force GMs in chess to teach me. 1800 they say is the requirement.
So, I shall try for 1800 . . .

Very approximately integer expression

Consider the following expression. This expression is an approximate integer generator.

In defense

Trade Secret

Drawing face, hands and legs first. Then drawing clothes is a cherished secret. I am letting it out.

Going advanced

I discovered the following with my expression (n^n)/((n!)^(n-1)) expression.
The expression was reduced to n/(((n-1)!)^(n-1)).
I obtained 40.000 while using √3/√2 instead of 1.2 of heart beats. I do not know what it means. But seems to be advanced stuff in numbers.
√2 and i periodicity sorts I think.
If anybody can help me further, I shall be thankful.

Happy pi day

The conscience and extroverted thing was not giving accurate results. I have a feel that research and devices are needed for accuracy.
However, I have considered heart beats in conscience and extroverted pi formula of mine and 3.14 value is obtained.
Happy pi day. 3/14.

#PythaShastri has Ramanujan type formula now

Remember, the formula for pi in Becoming Extroverted blog.
The formula was (2^(n(n+1)/2))/((n!)^(n-1)). I had given the explanations too.
It is tough to work like sun. So to say. Without emotion, without concern for others and doing your own thing. However, if you do it you get a function for pi. The above is the formula.
Now,
2^(n(n-1)/2) can be represented as C^n/(An+B). If I put this to the above equation, I will get an expression similar to pi of Ramanujan. I shall be working on this.
This was the last frontier.
So, Ramanujan famous pi formula can be compared.
Namaskarams, Ramanujan Sir in heaven. You did our country proud.

Ramanujan and I

I know quadratic equations. But higher order? No. Ramanujan knew.
I know simple calculus. Higher calculus? No. Ramanujan knew.
I know simple geometry. But higher geometry? No. Ramanujan knew.
Ramanujan was highly self learnt and practised a lot. He was a genius too.
Ramanujan would come up with numbers and expressions all of a sudden. And valid expressions too. Not error prone. He was accurate.
At Cambridge university he was encouraged for proofs.
Why  did he believe in goddess of Namakkal and not one of the deities of Kumbakonam?
Possibly his mother was from Namakkal region. His father from Kumbakonam.
He worked on numbers.  And number theories.
And that's what Indians can do. And we'll do numbers and their theories better. That's the challenge.

#PythaShastri formulas for Pi

Heegner Numbers

Learning Chess

I have the chess app in my Nexus tab. I played a lot of flight games using this tab, earlier. But now I no longer play the flight games. I play chess these days.
For about six months back till a month back, I could not play well. I was very easily beaten. I gradually picked up. Now I beat the tab in Level 3 too.
Chess is now interesting. Damn tough.But interesting. I have downloaded the ebook "The Application of Chess Theory" by Y P Geller.
I also watch opening moves in Youtube.
Middle moves are difficult. End moves are OK. But delayed. Defense is poor. I like attacking. But attack do not get materialized.
I strictly play at home only. Not in office.

Mathematical transforms

Yeah. That's what I am reading these days.
Extremely complicated, you may say. Yes it is beyond a common understanding. But then that is how I am leading my life.
I find it peaceful if I think in terms of equations. I believe transforms are happening in my mind plane.
I do not learn the transforms by heart. But I try to understand what the mathematicians think.
What are transforms ?
As I understand (-1)^n is 1/(2×n+1). And both express  even numbers.

#PythaShastri appreciates Madhava of Sangamagrama

More on #PythaShastri

Is #PythaShastri original ?
No, #PythaShastri is not original. All of the ideas are already talked about and written about by mathematicians. Euler, Madhava of Sangamagrama, Vacca and others.

So #PythaShastri is not original?
As written #PythaShastri isn't. However, #PythaShastri is genuine.

By genuine, I mean something like; an angle can be looked at in two ways. One will say acute. Others may say an obtuse angle. Both are right. Both the answers are genuine. And correct.

I just looked at certain things in numbers (and only numbers; not calculus; not algebra etc.) in one way and expressed them.

I believe, I have another expression for gamma inspired on the formula by Polka. However, I am not publishing the expression on Blogspot.

I think the scope for #PythaShastri is over now. These are the things that could possibly be done with numbers.

Goodbye, #PythaShastri. At least in the near future.

More on Vilvam tree

I had already talked on √2 based on vilvam /bael twig and its leaves.

The continued fraction was

[1,1,2,1,2,1,2, . . . . . . ]

It takes an expert to say that √3 is due to wind on √2 leaves.

What will happen when wind blows on a bael twig. The two leaves will make a namaste and come back to the original state.

Therefore the continued fraction of √3 is

[1,1,1,1,2,1,1,1,2, . . . . . .]

Hence proved.

Euler and #PythaShastri

First things first. Most of basic feelings of mathematicians are basic.
Euler talked on primes.
#PythaShastri had vision of measuring behaviour.
Euler was able to utilise primes in numbers in 3 ways. 2 for pi and 1 for Riemann zeta functions. For pi one method was - and + of primes in 1/n Riemann zeta functions.  1 point. Another was as products of primes and divided by nearest multiple of 4s. 1 point. Also he talked of 1/1- (1/P(k)). 1 point. 3 points.
#PythaShastri was able to utilise primes in 1 way. Decimal point. A sort of Riemann zeta functions. 1 point.
Euler gets  3 points and #PythaShastri 1 point.
Euler knew and expressed gamma. 1 point.
So Euler gets 4 points and #PythaShastri 1 point.
#PythaShastri did pi with own methods. 1 point.
Euler 4 points and #PythaShastri 2 points.
Differential are west-tech. They are events. Constant e.
Euler was greatest. I am reasonably ok as events methods usage.
No points to me here in differential, integral or logarithmic.
#PythaShastri has primes and combinations advantage courtesy measuring behaviour.
#PythaShastri can work on Ramanujan and Chudnovsky pi functions.
If at all I take chances. Or get a chance.
This finishes the topic.

Puzzle 2 - Rice Plate

Raghavan was a bachelor and was an interior designer. He came to Kolkata 40 years back from his village in south leaving behind ages of agricultural practice of rice growing.
Raghavan was asked by his boss to entertain six people with lunch on a Sunday. His boss told him that these six people were important and Raghavan need to serve them biryani and side dishes.
On the day of lunch, the six people arrived. Then they sat for lunch.
Where was the biryani bowl kept in the table ?

Puzzle 1 - Musical Chairs

Tarun was always chided by his wife Jaishree that he did not socialize much and was silent in parties. Jaishree wanted Tarun to be a star of parties.
Tarun realized that to win the heart of Jaishree, he needed to impress people attending these parties. Most of the parties had musical chairs competition and Tarun decided that he needs to win all these musical chair competitions to impress.
Tarun was highly intelligent and had a masters degree in engineering. He decided to make a plan for success in musical chairs competition. What could be the plan?

√2 and √3

√2 and √3 were known in earliest of civilizations and have been followed by generations.

0 to 1 (or) Riemann zeta functions is new knowledge.

Though I got involved in Riemann zeta functions, √2 and √3 are close to me and most of the constants are expressed by it, though to one or two places of accuracy only.

1. (√3+√2)/2 + (√3 - √2)/7 = 1.618 (phi)
2. 1/(√3 - √2) = 3.1416 (pi)
3. √2 - 3/4(√3 - √2) = 1.175 (side of a pentagon)
4. √3 + √2 = 3.146 (pi)
5. √3/√2 = 72/60 (heart beats)
6. √2/√3 *10/3 = 2.72 (e)
7. (√3 + √2)/2  - 1 = 0.57 (gamma)
8. (√3 + √2)(√3 - √2) =1

I hope to lead a better balanced life in future as far as mathematics is concerned.

Most beautiful constant

An increase of 1 from 1 will be an increase 2 times.
An increase of 1 from 10 will be an increase just 1/10.
I used to wonder about it. Is it fair. Is there an explanation.
About a year back, I discovered the answer. After discovery of Riemann Zeta Functions.
The number so aligns that the lower power numbers align with higher values. Euler made this equation. And the constant is called Euler-Mascheroni constant(γ).

γ = 1/2 (1/2²+1/3²+1/4² +. . . . . . )+2/3(1/2³+1/3³+1/4³+. . . . . . . . )+3/4(1/2⁴+1/3⁴+1/4⁴+. . . . . . )+. . .

The value of γ is 0.5772156649015328606065120 . . .