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.