Happy New Year Wishes

Here's wishing a happy new year 2019 to all my fellow bloggers and readers.

Chess rating 2000+

My rating has climbed up to 2013. You may recall that grandmasters are above 2500. Anand is about 2800 and Pragnanandha about 2500 plus. Nihal Sarin is a young prodigy who has promise according to Anand.

Carlsen is current world number 1. Kasparov, Karpov, Fischer are all time greats.

My rating has fallen down. I am trying exercises on general moves in opening and other moves. I am not good here. I have understood concepts of tactics, however. So the rating was high. But making better moves; it's not happening.

Chess king learn app

The last Pi

The basic pi generation algorithm (this is a pi generation formula and not a formula giving pi) is pasted below:-
1. (n!)/((n!)^n) factor was used. Extrovertedness. Jealousy.
2. comb(2n,n) factor was used. Measuring behaviour. Doubling.
3. 6/85. A rational number.
4. Iteration from 0 to 100.

Pi equation using staircase as simple machine is as below:-

1. (n!)/((n!)^n) factor was used. Extrovertedness. Jealousy.
2. comb(2n,n) factor was used. Measuring behaviour. Doubling.
3. ((n+2)^0.5)/((n+1)^0.5). Belief in irrational numbers. Staircase. Simple Machine.
4. 100000/860762. A rational number.
5. Iteration from 1 to 100.

In the first case 1/pi is generated to 5 places. In the second case 1/pi is generated to 8 places.

All I have to do is to take care of transcendental property of pi (I am not sure what I mean though !!). I need to develop that block and attach it to second case and generate further places of pi.

Pi and future plans

In future I shall be working only on (1+0.000041206)^n.

Got it completely. Used Chudnovsky factors for An+B/C. And 1/pi to possibly trillions of places. So jealousy and measuring behaviour are true.

Thanks Chudnovsky brothers. Great relief !!

The above is the closest I could get with my own applied integers.

Exercises these days

I was finding it difficult to lift 10kg dumbbells and do exercises these days. But dumbbells is what I like most for exercising.
I don't like free body exercises. So ruled out.
Walking was too easy. Cannot be called exercises.
Running/jogging was tough. So ruled out.
And yoga is something else. So is meditation.
So what did I do?
I bought 4kg dumbbells pair. And am doing dumbbells exercises. It is too light. But dumbbells are interesting.
The exercises. Deadlifts. Squats. Biceps curls. Overhead lifts. Side arm raises. Dumbell rows. Chest press. And leg cycling free body exercises.
Two sets of above.
I do them in the mornings.
I also do sandhyavandanam(religious prayers).
This is what I do in the mornings.

Pi expression

I had posted earlier that "Becoming Extroverted"(my blog) ideas result in sigma n!/(n^n). That is why this term occurs in faster pi expressions of Ramanujan and Chudnovsky brothers.
I am working on root 3 into sigma n!/(n^n).
The above results in 3.14 in just three iterations.
The equation has a scope and am further developing it. I am also trying to use "Becoming Extroverted" ideas in above to try and get further places of pi.
The screenshot of the last expression:

My final submission

1/pi to 10 places; the maximum my calculator can handle:

Divide 2.01........ by root 10. Divide again by 2.0031343434. You get 1 by pi. 

I believe the last

Growth of a rational number

I am giving a formula for growth of a rational number. This formula is accurate.
Growth of a rational number p/q is
2(q-p)(1/((q+1)^2)+1/((q+1)^4)+1/((q+1)^6)+. . .)
Application of growth of rational numbers:-
Rice/Cereal production.
Tiger/All animals ratio.
Hindi people/Total Indian population.

With this I conclude my number theory endeavours. This was a final desire to express.

Continued fraction for pi

I am happy that my series 1,3,6,10,15,21 . . . has proven to be good. For the past few days I was thinking that it failed in the classic weights and scale problem ( the problem was what weights needed to measure any weight upto 100 kilos?). 1,3,6,10,15,21 . . . was great in rational number series. But it didn't do well in the classic scale and weights puzzle it seemed.
But 1,3,6 were good in upto 10 kilos category.
And 1,3,6,10 were good in upto 20 kilos.
But upto 100?
Then I thought about
1,3,6,
10,30,60,
100,300,600,
1000,3000,6000
And then it seemed to fit.
This is one solution to the classic scale and weights puzzle.
5 weights are needed in 3^n series.
6 weights in 1,3,6,10,30,60
7 weights in 2^n series.
This finished the puzzle.
Well the above gave me some satisfaction and I worked a continued fraction for pi.
I think 11 pi = 100÷(2+2^2÷(3+3^2÷(4+4^2÷(5+5^2 . . . . .

Taylor series for 1

Taylor series for 1 is
1/2!+2/3!+. . .
Taylor was a Scottish mathematician.
There is another interesting continued fraction for 1.
1 = 3÷(2+5÷(4+7÷(6+9÷(8+11 . . .

Claims

Apologies

I deeply apologise for using the tag #PythaShastri. I used this tag because it was true in my nature.  Secondly I wanted to reduce ego. And the third reason is as a prayer to God.
Pytha had two meanings. Pythagoras and pythium(tamil word meaning mad). Shastri is a Brahmin or a learned man ( Indian meaning passed over ages).
I will definitely not be using this tag ever from now onwards.
But before that I make the following claim:-
"I bet 1000 to 1 that the series 1,3,6,10,15, . . . is the best series if we have to use numbers for estimating."
You can argue with 1,2,4,8,16 . . .
Or argue with 1,1,2,3,5,8 . . .
(Mathematically odd series 1,3,5,7 . . . and even series 2,4,6,8, . . . do not fall in the argument as they are manifestation of natural numbers)
So first of all do not be confused. Leave the natural number series alone. And think about the other series. And consider my claim.
(Hint: You can use the classic scales and weights puzzle here. The puzzle was what are the weights needed to weigh any weight upto 100 kilos?)
In simple words, I claim my method may be the best one.

Plans to be a Class A chess player (ELO rating of 1800 - 1999)

I am planning to improve my chess.
I plan to increase my ELO rating to 1800 in three months time. With this objective in mind, I have bought a Kindle ebook "5334 Problems, Combinations and Games" by "Laszlo Polgar".
I am confident that with this book I shall definitely achieve my objective. 

#PythaShastri constant P

#PythaShastri ( #PythaShastri is Ganesan Kirtivasan) is advocating a constant P.
P is similar to golden ratio. A very slight change.
P occurs in nature.
P is irrational.
1,3,6,10,15,21,28,36,45 . . . . is the real number series.
1/2,3/4,5/6,7/8,9/10, . . . is the rational number series.
3/4-1/2 = 1/(4×1). 1 of 1,3,6,10,15 . . .
5/6-3/4 = 1/(4×3). 3 of 1,3,6,10,15 . . .
7/8-5/6 = 1/(4×6). 6 of 1,3,6,10,15 . . .
. . . . .
. . . . .
P is calculated similar to golden ratio.
3/1 then 6/3 then 10/6 then 15/10 and so on.
I have calculated and it converges at 1.02.
P is approximately 1.02.

#PythaShastri and any rational numbers

India needs formulae in demographics. Not in trigonometry or logarithms.
Rise up India!! Before it's too late. We are to be the most populous country in the world. Help is needed. Give help take help.

My learnings

Chess
Chess is tough. Damn tough. By constantly playing in tab and over Internet; I have realised my elo rating is about 1400. But my moves are not effective.
There are two things to do to win always. First dominate the middle four squares. And extend your pieces to maximum(youtube). It is fine provided your opponent is dumb!! I am not criticising but appreciate that this is the way to win. But you need to develop your pieces accordingly.

Mathematical series
I have done well, I think. But great mathematicians may dismiss my discoveries as "already known" or "results of cusps of numbers" or "number field results".

Cartooning and caricatures
This may fetch results. I am confident. But I need to be accurate and practice on accuracy and theory.  I can achieve a little here. I am confident.

Music
My dafli is in my heart. The rhythms are always there. I had a good singing voice while I was in Delhi. I have lost singing ability in last two and half years. At the most I can compose and sing India type songs. But enthusiasm has got lost.

#PythaShastri π/4 series

π/4 = 1/1 - 1/3 + 1/6 - 1/10 + 1/15 - 1/21 + . . . . . . . .

What are these 1, 3, 6, 10, 15, 21 . . . . . . .  ?

These are numbers from #PythaShastri pattern. Please refer to #PythaShastri pattern posted earlier in this blog. It was a brilliant ( it seemed to me !!) pattern between rational numbers and a series of natural numbers.

And now it seems to be approaching π/4 when expressed in denominators with + and - signs alternated. I have not checked it completely. But two places 0.78 was approached.

π/4 is tough to reach. Madhava of Sangamagrama gave a series of π/4. My measuring behaviour equation gave π/2. Then there was one π/3√3.

You may think I am being proud. I am not at all proud but I am writing so in praise of God.

Contentious #PythaShastri

Numbers are really complex. My favourite statement in numbers and number theory is "There is no 2".
Numbers and number theory gives a lot of insight. Greed, desires, ambition analysis. The advantage with numbers is greed, desires, ambition can be quantified and expressed as an equation.
We (India) have been following a statement like there are 15 people in my department. We must express in rational numbers like 8/7 or 15/8 or 15/7. (There are 8 north Indians and 7 south Indians).
Imagine there are 15 bags of cereals. 4 of them are wheat. 15/4 now. If 1 wheat bag is taken away it becomes 14/3.
Then there could be squares and square roots of rational numbers. Possibly fear or rumour analysis. Or sex pattern.
In short, rational numbers are the way for Indians to move ahead. Especially when India is going to be the most populous country.
#PythaShastri has formulas for rational growth. Of rational squares and rational square roots too.
It is time #PythaShastri (Ganesan Kirtivasan) gets a chance.

Caricaturing and Cartooning

I have finalised my styles in cartooning and caricatures. By finalised, I mean that I have reached satisfaction level with the amount of skills I have. As an example, I am confident of scoring 95 percent or above in class 7, let's say. There is no meaning in comparing with class 8 or 9 student.
There are three greats in caricaturing, cartooning and animal drawing. They are:-
1. Tom Richmond - Most outstanding caricatures. A picture they say is worth 1000 words. Tom Richmond's caricatures are worth 10000 words.I have his Mad book on caricatures bought with money.
2. Lou Darvas - Fantastic cartoons. The limit in expression and using angles. Damn great work. I have his e tutorials bought with money.
3. Ken Hultgren - Wow. So great lines. The 3d, the angles and action comes so easily to him. I have his e book downloaded from internet for free.
In India, Raj Thackeray is simply great in cartoons and caricatures. A style which makes me mad with admiration.

#PythaShastri pattern

#PythaShastri past, present and future

#PythaShastri doubts

#PythaShastri root 2 series

#PythaShastri root 2 series.
Well the past few days has been turbulent. There were a few discoveries over the last few years. Rational expressions. Euler - Mascheroni expressions and pi and e.
I am interested in Fourier. And Ramanujan. And Euler.
But then in my expressions the root 2 expressions were missing.
I decided to express in my known methods. And it was happening. Here are they:

An era of expressions to my satisfaction is over now. Further studies are no longer to be in this approach. I plan to study methods and techniques of mathematical expressions. Not results. But methods. This is tough as it is to get an insight into the minds of mathematicians. But I shall try to.

#PythaShastri 4 screenshots

#PythaShastri 4 screenshots.
1, e, gamma and exponential integration.

#PythaShastri max rep series 2

#PythaShastri max rep series 2.
Experiment details are :

Two way correction to #PythaShastri series

#PythaShastri how much worse can it be

#PythaShastri max reps series

#PythaShastri max rep series.
The following are experiment details:

#PythaShastri and Euler line

#PythaShastri and Euler line.
Results are :

Khinchin constant

Happy Independence Day.

#PythaShastri Gamma Expression

#PythaShastri gamma expression. The Euler-Mascheroni constant.

I don't know whether the meaning or the expression is correct. Euler-Mascheroni constant is extremely subtle. However here is a screenshot of Euler-Mascheroni constant from Symbolab:

Dr. Vashist Narayanan Singh, Bhojpur

Dr. Vashist Narayan Singh is a very simple man. Living in rural India.
He is very highly qualified. Graduation from Patna, Bihar. And more.
Among possibly many points to ponder; he very rightly wants (a+b)^2 = abcd.
I saw him in Youtube.

#PythaShastri prime number sieve

1. Let current number be x.
2. Let x +1 be y.
Two variables needed.  x and y.
For any range prime number sieving do the following models:
1. Check divisibility of x by 2.
2. Check divisibility of x by 3.
3. Check divisibility of y by 4.
The above are the only methods needed.
Further steps are worked out.
By the way, I have registered copyright on two pi expressions.
( I don't like copyright or patents. But then . . . )

#PythaShastri √3 formula

√3 = 3 √(1/4 + 1/4² + 1/4³ + . . . . . . . . . . . . . )
Root √3 has been expressed. This finishes #PythaShastri endeavours.

Also I think
√3 = 3 √(1/2 - 1/2² + 1/2³ + . . . . . . . . . . . . . )

#PythaShastri points to think

Here are they:

And more . . .