Doing Fine

Art
In art I have bought charcoal pencils. There are three pencils hard, medium and soft. These are best for caricatures. For cartoons black gel pens. I am a black and white guy in art.

Mathematics
I have got another paper published in JETIR. I shall complete all formalities and shall later provide a link and write details.

Music
I have done a lot of research on taals and have adapted dafli playing to Indian taals. I shall write about it later.

I am in Delhi now. But shall be in Ranchi for new year.
My new year wishes to my blog readers. May all the good things happen to you in the new year and beyond.

Citizenship Amendment Act

First things first.
I don't think the general public is aware of a thing called citizenship. What the hell? All are citizens of the country. Then what is citizenship amendment?
It seems to be a foreign ministry act. Not a home ministry. To me. Mr. Jaishankar should be presenting it. And not Mr. Amit Shah.
Our DMK leader has opposed it.
But the President has okayed it.
Now as a citizen of India if Narendra Modi feels it is the role of science department to consider me in mathematics, then Narendra Modi also should think whether it is home ministry or foreign ministry who should be putting the CAB. My view is my mathematics is really very good.

A good tweak this one

I listen to songs based on habit. I don't easily like latest songs. However I do like the playlists of Google play music and others. I like their categorisation of latest pop, latest bollywood songs etc.
However, many times I am moody. At a particular moment I just have to listen to a song by Ravindra Jain for instance.
The solution that worked for me for the last few years was storing songs in mobile. And listening to playlists offered by Google play music.
Recently a brainwave occurred. I put all my songs (about 1000) in Google drive. But opening the songs and playing the songs over bluetooth did not happen when I opened google drive in browser.
So what I did was install Google Drive app. Bluetooth playing of songs now happen!!
So Google Drive and Google Play Music apps are my way now to listen to music.
I have Philips bluetooth speaker.

Self - Guru

I do not comment on master artists much. Like Andrew Loomis, for example. However I do recommend their names. I do not comment because I may be different than the master and I do not wish to comment making my own suggestions.
The idea below is my very own. So I am attaching the paper.

Paperless Society

What is not being Paperless?

1. Scanning paper and posting the scanned paper to server and keeping both the paper and scanned image is definitely not being paperless.
2. A non-collaborative writing in office in a piece of paper is not moving towards being paperless.
3. Writing opinions in a piece of paper without data supporting it is not moving towards being paperless.
4. A write-up lacking clarity and which does not have block-diagram or a flowchart when required is not moving towards being paperless.

What is moving towards paperlessness ?

1. Using Microsoft Office in collaboration
2. Using OpenXML standards
3. Using Microsoft charts in Microsoft Office documents 
4. Having Office online and a big name over Internet

Mathematicians

What comes to my mind

I have great quality in mathematics. Karpov level.
I am in a position to read Euler. And understand German mathematicians.
I thought of taking up charcoal drawing. Because my interest was in faces. But then I restricted myself to pencils. Did not buy charcoal drawing set.
Then I need to study perspectives and draw better folds in drawing.
Chess improvement is almost impossible with chess game app. I need to play with people.
In dafli I am planning to increase the number of dafli fills.
Violin, guitar interests have faded. Completely.
Partying was never my interest. Get together is also nil.
I can think of many things like self grooming, car cleaning and home maintenance etc.
Have a nice day, dear readers.

Caricatures improved

I was practicing on caricatures these days. I was not comfortable with the 3d look in them and followed Andrew Loomis method very carefully. Thanks to Andrew Loomis for his wonderful book "Drawing head and hands". The book is excellent and it took a while to pick up his concepts.
Now I am a bit more confident.
So, here is some caricatures I drew today:-

Caricatures

I always drew caricatures with face facing straight. Then today a thought came up. I was always confident in side views. But straight I was not. Then I thought mix these two and draw 3/4 views.
The above caricatures I made just now. From memory. The above have simple lines. But I plan to extend them to highly complex 3/4 views. In coming months.
So I have frozen my art desires. Caricatures 3/4. Cartoons.
Best wishes to all of my blog readers.

About some pi expressions

Most of the formulas for pi are based on mathematical functions. But a few of them are not. These are driven by intuitions and are based on numbers, prime numbers or square roots.
Here are some of them :-

Two of them from Euler. And one from Viete.
Yesterday evening I was thinking hard on root 2, root 3, root 4 . . . . . . etc.
Then I found that

The 12th term was 0.25908. The 13th term was 0.52634. Their average is 0.39271. And 0.39271 is about pi/8.
The results in Wolfram from root(2) to root(5000) and root(5001) are:-

The average sway is (0.40217207+0.38803135)/2 = 0.3951017. It is pi/7.95135.

So the sway remains at about pi by 8.

Indeed the Gauss Error Function observed here.

Rediscovering 1,3,6,10 . . .

1,3,6,10,15 . . . already exists. 1,3,6,10,15 . . . is the triangle series.
I didn't know that. I rediscovered it. I applied rational growth and made some formulas. So the series was rediscovered.
I found another thing yesterday. The square series 1,4,9,16,25 . . . relationship with 1,3,6,10,15 . . .
Subtracting term by term each of the numbers of square series with the triangle series creates a series of terms 0, another triangle series.
1 - 1 = 0
4 - 3 = 1
9 - 6 = 3
16 - 10 = 6
25 - 15 = 10.
and so on . . .

Mathematical Philosophy continues

Before one takes any step one should outline steps of thinking. The deepest steps of my thoughts are:
1. There is zero. Vortex. Gravity or human driven.
2. There is basic c. Complex number center.
3. There is z. Human complex interpretation.
4. There is area. The beginning.
And/Or
1. There is zero. Vortex. Gravity or human driven.
2. There is basic c. Complex number center.
3. There is z. Human complex interpretation.
4. A division. 2 and 2. Or 1 and 1. Bi-directional.
And/Or
1. There is zero. Vortex. Gravity or human driven.
2. There is basic c. Complex number center.
3. There is z. Human complex interpretation.
4. A delta triangle. 3 and 1. 3 are sides. 1 is direction.
All the three are important. And are sort of recursive.

My truth is of and for Indians

I wrote about Laurent Series and the completion of a round in a sports track and beginning of 1.
I feel Abel transform is similar to Laurent series in some way.
Also, Harishchandra (Indian mathematician) transform is similar but in parabolic form.
My point is this. I am talking of an India which I see.
Only if you have food can one complete a round around an olympic track.
My # expressions is not about completion. It may be imagined as height by length. And growth there in.
So according to my model if the villagers of Kalahandi (where people died due to famine) had a good relationship with Tanjoreans (rice growing area in Tamil Nadu) which is a rational number; and this rational number had grown then the death at Kalahandi could have not happened.
I am quite serious when I am writing this.
Please support me.

The beginning - Laurent series

Carl wants to count the number of rounds of the olympic track he is able to complete by running.
Tracy is observing and counting.
Only when Carl encloses an area does Tracy begins the count with 1 round completed.
So there is an area. There is n. There is n+1(next round).  There is periodicity(sigma series). Then there is the beauty in Laurent expression. 

Now What?

The mathematics I was writing about is over.
But mathematics is a big field. There are areas like discrete mathematics, algebra, calculus in detail, set theory,  hyperbolic geometry, algorithms etc. So a lot of scope exists for everyone.
I would be reading more from "Theory of Complex Functions" book.

Pentagon and heptadecagon

A side of a polygon is 2a× sin(180/n) where n is the number of sides of a polygon.
When I drew a pentagon I used the formula
Root(2) - (3/4)(Root(3) - Root(2)). This requires only a compass. 1.175 is the side length of a pentagon if radius is 1.
Then I read in Wikipedia that as a kid Gauss drew a heptadecagon (17 sided polygon) using a compass. The full name of Gauss is Johann Carl Friedrich Gauss. Gauss was a child prodigy and made contributions due to which he is considered "the greatest mathematician since antiquity". He was also called "the foremost of all mathematicians". The erstwhile cgs unit of magnetic flux density was named after him. Gauss. Many web sites over internet say Gauss is the "Prince of Mathematics". And the "King of Mathematics" is Leonhard Euler.
Well I tried the adaptation of heptadecagon with a formula similar to pentagon.
(Root(14) - (3/4)(Root(15) - Root(14)))/10. Dividing by 10 needed here. (This cannot be obtained with compass. Dividing by 10) In a pentagon 5 you had 2 & 3. For heptadecagon 17 you have 14 and 15.  The value is 0.364 while actually the value is 0.367. The side length of heptadecagon if radius is 1.
So a similar formula for both pentagon and heptadecagon exists. However dividing into 10 is not possible with a compass only. One needs setsquares or drafter. Anyway this method of mine needs a very large paper.

About Ramanujan

Ramanujan was a great mathematicians. I have no doubts about it. He made what are now known as Ramanujan theta functions, Ramanujan tau functions and Ramanujan Sato series.
I have applied myself and have explained these three important functions in my blogs.
Ramanujan had made great contribution in partition of numbers. Eg. 4 can be expressed as 4,3+1,2+2,2+1+1,1+1+1+1.
Now, my series of 1,3,6,10,15 . . . is a special case of partition. 1,1+2,1+2+3,1+2+3+4,1+2+3+4+5, . . . .
I have demonstrated the importance of 1,3,6,10 . . . in my blogs.
So partition of numbers as an Arithmetic Progression is important.
I have demonstrated the growth of rational numbers too.
Partition of numbers in Arithmetic Progression and rational number growth have a connection.
I am interested in further studies and/or work.

The Kashmir solution

Let us understand history and early British plans.
Sir Radcliffe and Lord Mountbatten partioned India. Accession of individual kingdoms and provinces to  India was essential. Most of India was made that way. The king of Kashmir accepted India. Then there were important foreign presence provinces and structures like places in Goa, Pondicherry, Chandigarh, Delhi which were made union territories.
Now since Pakistani flag and Pakistani presence is high in Kashmir; the Government of India has rightly made union territories in the state of Jammu and Kashmir as Pakistan is a foreign country.

Looking back and ahead

I am back in Ranchi.
It was in November 2010, that I made the blog Measuring Behaviour. During those times I managed to express pi approximately as 22/7. I also had expressions on the mathematical constant e. Frankly there were two things that I wondered. 2n and n. World is unfair(n). World is fair(n). And you measured the behaviour(2n). Gradually I started expressing better. I made a few infinite series expressions. And currently I am with the book "Theory of Complex Functions". Hoping to learn the methods and lemmas.
Later, I realised you have to consider unfair(n) and fair(n) together for measuring behaviour(2n). Expressing in terms of infinite expression, I got

Later I fine tuned and got better pi expressions. These are

I later realised that comb(2n,n) is great in expressions of irrational numbers too. I got

Since I got root 5, I expressed the most famous golden ratio. This what I got

Now. As I wrote above, unfair(n), fair(n), measuring behaviour(2n) is important. But one cannot deny that one looks at the world with only one thing in mind. Either fair. Or unfair. Is it not?
So I tried n and 2n. This is what I got

This has opened a new world to me. For one when dealing with n and 2n and not n,n and 2n, you get an expression which has both pi and e terms. In one expression you have both pi and e in the numerator and in the other(alternated negatives) you get pi in the numerator and e in the denominator.
This gives a lot of insight into the behaviour of a man. If he looks at the world as unfair or fair (one of these) he gets an equation which is absolutely different from if he looks at the world as both fair and unfair, both together.
I am also pasting the definition of error function (of Carl Friedrich Gauss) and that of imaginary error function too.

Away to Delhi

I shall be away from Ranchi; shall be going to Delhi. Mother and myself. Personal reasons.
I have to get some of my gadgets repaired.
Buy drawing ink and black drawing pens.
And more . . .
Matar kulcha. I look forward to.
I may be inactive in blogs for a while.

A jump above Youtube

What can an Indian do at the most?
Youtube.
I was in Sylvania and Laxman limited as a sales and service engineer. I was attracted to lighting design. It is a course in itself. Tubelight emits light of a frequency close to daylight. Tubelight has a tough circuit. The choke and the starter are in series with tube which has tungsten filaments on two sides of tube. Tungsten is a costly element. Tungsten has both heat properties and UV arcing properties. My imagination grows and grows. Car distributor, spark plugs, tubelight, lamps, leds etc. Then chokes, electronic starters, raman effect, fourier transform etc. My world is made.
Please forgive me if I am wrong Samsung. Hopefully my salary is made.
The salary is the jump above Youtube.

Movies by Anurag Kashyap

Movie making is no easy thing.
Production houses have to line up so many things. Stars and motivation. Scheduling. Budget. Quarrels handling. And more.
Directors have to get the whole idea materialised.
I feel the role of art director is toughest.
Then the role of screenplay writer.
I have not seen a single movie made by Anurag Kashyap. I think he must be really good. Especially Ugly. It is a thriller movie. And I want to see this movie.

Gauss -Legendre pi

Sylvester Medallist 2019

Professor Peter Sarnak FRS 

The Sylvester Medal 2019 is awarded to Professor Peter Sarnak FRS for transformational contributions across number theory, combinatorics, analysis and geometry.
Professor Sarnak will be awarded a medal and a gift of £2,000 at the Royal Society's Anniversary Day meeting on 29 November 2019.

To think about it . . .

" . . . . To think about it the whole thing could have been avoided(Bombings that ended World War II). It is almost as bad as the man who wrote Mein Kampf". Wow !! Humour !!
It should have been BSc maths at Delhi University. Percentage needed was also less than BSc physics. Jhel nahin paate.

Riots

The whole town is burning and is on fire,
The result of the two communities ire;
The other is wrong and we are right,
Let us settle with a fight.

The secret of evil is in its continuity,
Moving on and on till infinity;
A woman to me is an infinite series,
Not joking at all and am serious.

Maybe then a solution is in sight,
To control riots and make things all right;
This maybe an answer and let civilians take cover,
Lady policewomen you take over.

Movies with broader appeal

I recommend the following movies to watch and enjoy in your weekends.
1. Drishyam
2. Kahaani
3. 8 x 10 Tasveer
4. Suraj ka saatvan ghoda

Kulikarai - A Short Story

Vasudevan was sitting nervously in his 2nd AC coach seat. He was shaking his head left and right every five minutes or so. Not that he was disapproving anything in particular but he gained this habit recently and his wife admonished him on several occasions for this habit of his.
Opposite to him was a man who was aged and looked decent. The man started the conversation with Vasudevan. He said, " I am Dr. Selvan. Retired surgeon from Vellore medical institute. I am on my way to Sundereswarar temple to offer pooja. What about you ?"
Vasudevan replied," I am Vasudevan, newspaper distributor in Warangal. I am also on my way to Sundereswarar temple. To offer pooja for my son who is in 12th standard."
Dr.Selvan then offers some fruits from his bag to Vasudevan.
Vasudevan refuses the fruits offered by saying," Actually my son needs all the nutrition. This is a crucial year for him. And it does not suit my persona if I eat fruits alone.".
Dr. Selvan then says," I have one daughter who is married and is in USA. My wife is no more and I lead a life shuttling between USA and India.."
Vasudevan replies,"My wife works in a MNC. She is doing well in her career. I wanted her to quit her job and take care of our son who is in crucial year. Well, she refused. She continues to work."
Dr. Selvan then observes Vasudevan shaking his head left and right.
Dr. Selvan and Vasudevan kept talking with each other. They seemed to enjoy the conversation and it suited them because it helped pass time in the train.
Suddenly the train stopped. Possibly for signal. Vasudevan could see the concrete board of the station. It was Kulikarai. A town perhaps.
Vasudevan thought of getting down and take in some fresh air. But he did not move. He thought why take a chance. The train might move. After about a minute, he again thought of getting down. Again he did not. No point. The train will move any time, he thought.
After about two minutes Vasudevan stood up and started moving towards the door. He wanted to get down to breathe in fresh air.
Suddenly the train moved. Vasudevan had his foot on the steps at that instant. He lost balance and fell inside the train. His head struck the steel door handle and he shouted, "Aiyo, aiyo".
Dr. Selvan on hearing cries, rushed towards the door. He helped Vasudevan to stand up and slowly they came back to their seats.
Dr. Selvan then said,"You have bruised your head slightly. I shall not apply anything on the bruise. However, you must eat this tablet." And he offers Vasudevan a tablet.
Vasudevan could not understand. He asked," Why a tablet when I have a minor bruise?".
Dr. Selvan replies," I have been observing you all the while. And the tablet is more important to you than an ointment for the bruise. You are suffering from high anxiety."
The train gave a whistle.

Fourier Series

The two idiots

This poem is based on the movie "The 3 idiots". It was written by me during those times. I am publishing in Google Blogspot today.

The two were the best of friends till then,
A heated argument broke them up just when;
They promised to meet in ten years,
To see who is better and who is in tears.

One of them was a guy of high financial wisdom,
He saw money in areas where no one could fathom;
The other was great in mathematical matter,
Measuring before and taking steps after.

It is ten years now, from that damned day,
Where and what are they very few could say;
But will they ever meet? For sure yes;
Each to show his own success. 

The crap continues

As I wrote earlier in my blogs, there is no 2. Meaning no two things are similar. Riemann thoughts.
But we do have two hands, two legs, two eyes and two ears. Complex number
So let us say the human started to wonder. He started saying 1,2. He felt it as doubling. And also the human wondered 1,2,3,4,5,6, . . .
Basically the human wondered. Differentiation.
The human wondered 2,3,4,5. He then questioned and said 2,4,3,5. This is important.
2,4 is correct sense from 1,2. Doubling.
So why not 2,4,3,5.
2,4,3,5 gives many things.
1. Doubling.
2. Pythagoras laws 4,3,5.
3. 2,4 are closer. Even number concept. cos series.
4. 3,5 are closer. Odd number concept. sine series.
So a simple thing like five numbers gives an ocean of things to wonder about.
I have in fact not touched the thumb. Right angle.
The four fingers together with thumb. Ampere's right hand rule. (I am defeated here. Physics.)
The three finger Fleming's rule.(I am defeated here. Physics.)
Got it. Heard, heat and electricity are similar. So must be Fourier and Ampere. Thanks. 

Death by W B Yeats

Nor dread nor hope attend
A dying animal;
A man awaits his end
Dreading and hoping all;
Many times he died,
Many times rose again,
A great man in his pride
Confronting murderous men
Casts derision upon
Supersession of breath;
He knows death to the bone –
Man has created death.

Energy and Water

Energy
Energy is tough. It is so easy to buy an AC or a car. But the implications of such a decision is phenomenal.
Travelling by bus or metro may not be a solution as bus or metro has to take your load. Consider taking leaves.Work from home for ladies and handicapped should be considered. Shifts in government offices should be considered. If husband and wife work in the same office, they should get company benefits.

Water
Water is about neutrality. Every person is expected to be neutral and analyse things in a neutral frame of mind.
Better style in communication and tolerance should be promoted. Gender equality should be promoted. Managing the pluses and the minuses, both, should be encouraged. Jealousy and condemnation should be discouraged.

My feeling is if Up and Working is high then Energy and Water can be allotted as per shastras and teachings in upanishads.

If Zero Laziness is high then Water can be allotted as per shastras and teachings in upanishads.

Circle, square or 12

Tal Guppa - A Short Story

Ramesh was sitting comfortably in his 2nd AC coach. He was a manager in a reputed government undertaking and was earning reasonably. He was confident he can manage education of his son and can marry off his daughter comfortably with the salary he earns. He was on an official tour and was travelling in 2nd AC coach as per his eligibility.
Ramesh, however did not have much work in his government office. Most of the time he would sit idle in his chair and would act as if he is doing something significant when his bosses came into his room.He also was not happy with the monotonous life. He took bath at 8 am daily. Then would pray for 30 minutes before leaving for office. In the evening he would teach his kids and then would go to bed after dinner. This was the life he was leading and he was unhappy because of this monotonous life.
It was 5 pm, evening time in the train and Ramesh was enjoying the sight of the villages and farms. Suddenly the train stopped. Possibly for signal. He looked out and could see that the train was in Tal Guppa, a small town probably. Ramesh could see some farmers toiling hard in the fields near the station.
Ramesh decided to get down and enquire the farmers toiling hard about their lives.
He gets down the train and after crossing the tracks and the platform, he reaches the fields where the farmers were toiling.
Ramesh then casually asks them, " How is life?"
One of the farmers says, "Each day is challenging but exciting. We have to work hard for water, fertilizers, crops and other things every day. Not a single day is same. We like working hard and look forward to challenges every day in the mornings"
Ramesh then thought that the life of the farmers was exciting and was just the opposite of his daily life.
The train gave a whistle and was about to move.
Ramesh was standing in the fields contemplating on leading a farmers' life.
The train began to move slowly. Ramesh then asks, " What about money?"
The farmer replies,"Money is tough. We are barely able to lead a comfortable life. Though crop insurance are there, they are only for name sake."
Ramesh stood there for a couple of seconds. A farmer's life. Or a government servant. The train had already started to move.
Then he decided. And started running towards the train. As fast as he could. He came near his compartment. He reached out for the iron bar door railings. He could manage to grasp the iron railings. Then he swayed his leg towards the steel steps. His feet landed on the step. He was lucky. He opened the steel door and went inside for his seat.
Once in his seat, he gave a sigh of relief. He took about 5 minutes to get back his breath.
The train gave a whistle.

Drawing Materials

The above are the drawing Materials that I have.

Nihal Sarin - 2600 rating

The boy on the left is Nihal Sarin. On the right is Praggnananda.

Here is a clip from Indian Express

"The Grandmaster from Kerala became the youngest Indian to cross the 2600 rating after earning a draw against GM Liviu-Dieter Nisipeanu in the second round of the TePe Sigeman & Co International tournament underway in Malmo, Sweden. He is also the third youngest in the world to achieve this feat.
"I don't have much to say about getting to the 2600 rating. I am happy but more work needs to be done. I should improve more." Sarin told . . . . . . ."

Any time exercises

Any time exercises are exercises which are very motivating to the body. Motivating enough to do anytime.
The following are my any time exercises :-

1. Squats
2. Biceps curls

In that case . . .

Colin Maclaurin gave sine, cosine and other trigonometric series.

Leonhard Euler must have discovered sine and cosine series himself and used them in e^i. theta.
If someone says Euler copied Maclaurin; I don't get disturbed.

I say that then Gauss is the king. Gauss seemed to be very high in favor of complex functions. Here is what he wrote. He wrote in German. Roughly translated in English he meant

"Complete knowledge of the nature of an analytic function must also include insight into its behavior for imaginary values of the arguments. Often the latter is indispensable even for a proper appreciation of the behavior of the function for real arguments. It is therefore essential that the original determination of the function concept be broadened to a domain of magnitudes which includes both the real and the imaginary quantities, on an equal footing, under the single designation complex numbers."

I believe in, "When your stomach is hungry, your hand reaches for food.".

Leonhard Euler is known for quality and quantity. His e^(i.pi)+1=0 is considered the best equation so far.

So, Leonhard Euler is the king of mathematics.

There is Euler-Maclaurin formula.

I believe in and too small in front of Reinhold Remmert. Reinhold Remmert says

"A.L. CAUCHY (1789-1857), B. RIEMANN (1826-1866), K. WEIERSTRASS (1815-1897). 

Each gave the theory a very distinct flavor and we still speak of the CAUCHY, the RIEMANN, and the WEIERSTRASS points of view. CAUCHY wrote his first works on function theory in the years 1814-1825. The function notion in use was that of his predecessors from the EULER era and was still quite inexact. To CAUCHY a holomorphic function was essentially a complex-differentiable function having a continuous derivative. CAUCHY's function theory is based on his famous integral theorem and on the residue concept. Every holomorphic function has a natural integral representation and is thereby accessible to the methods of analysis. The CAUCHY theory was completed by J. LIOUVILLE (1809-1882), [Liou]. The book [BB] of CH. BRIOT and J.-C. BOUQUET (1859) conveys a very good impression of the state of the theory at that time. Riemann's epochal Gottingen inaugural dissertation Grundlagen fair eine allgemeine Theorie der Functionen einer verdnderlichen complexen Grofle [R] appeared in 1851. To RIEMANN the geometric view was central: holomorphic functions are mappings between domains in the number plane C, or more generally between Riemann surfaces, "entsprechenden kleinsten Theilen ahnlich sind (correspondingly small parts of each of which are similar)." RIEMANN drew his ideas from, among other sources, intuition and experience in mathematical physics: the existence of current flows was proof enough for him that holomorphic (= conformal) mappings exist. He sought - with a minimum of calculation - to understand his functions, not by formulas but by means of the "intrinsic characteristic" properties, from which the extrinsic representation formulas necessarily arise. For WEIERSTRASS the point of departure was the power series; holomorphic functions are those which locally can be developed into convergent power series. Function theory is the theory of these series and is simply based in algebra. The beginnings of such a viewpoint go back to J.L. LAGRANGE. In his 1797 book Theorie des fonctions analytiques (2nd ed., Courcier, Paris 1813) he wanted to prove the proposition that every continuous function is developable into a power series. Since LAGRANGE HISTORICAL INTRODUCTION 5 we speak of analytic functions; at the same time it was supposed that these were precisely the functions which are useful in analysis. F. KLEIN writes "Die grofle Leistung von Weierstrafl ist es, die im Formalen stecken gebliebene Idee von Lagrange ausgebaut and vergeistigt zu haben (The great achievement of Weierstrass is to have animated and realized the program implicit in Lagrange's formulas)" (cf. p.254 of the German original of [H8]). And CARATHEODORY says in 1950 ([5], p.vii): WEIERSTRASS was able to "die Funktionentheorie arithmetisieren and ein System entwickeln, das an Strenge and Schonheit nicht iibertroffen werden kann (arithmetize function theory and develop a system of unsurpassable beauty and rigor)."

All time expressions

Prime numbers generation formula

True Love or Mahabharata or I try so I write

A maternal uncle's love for his nephews is true love. And also equal for all his nephews. Amazing!!
Krishna was born to teach maternal uncle Kansa a lesson for not being like that.
. . . . and the foundation of the epic of Mahabharata was laid.
And here is the link to Ramayana. My thoughts. http://theotherday-kirtivasan.blogspot.com/2018/07/devas-monkeys-and-not-so-humans.html?m=1

Bobby Fischer Chess King course

I had already downloaded Alexander Alekhine Chess King course.
Most of the course material are theory and mainly chess moves like e5,Qd6 etc.
But then I wanted Bobby Fischer course. I feel Bobby Fischer is about IQ moves. Alekhine is about Chess principles.
I wanted Chess Principles only. But then . . .

Alexander Alekhine Chess King Learn app

My chess game is improving. And chess is a money generator sports activity in India. I want to venture into this field.
My basic moves are strong. I can play good moves. But better moves and genius moves are not happening.
This calls for theory and practice on theories.
I had to choose one chess great from the list available with Chess King App.
I was focussing on Bobby Fischer, Alexander Alekhine, Vishwanathan Anand and Gary Kasparov..
Then I made my choice. Alexander Alekhine.

My political stance

Elections are approaching. Currently my stance is Aam Admi Party, DMK and therefore Congress.
I do not like Indian society much. But I like India very much.
As India is going through tough times; I thought I must write what I think.

AI Factory's Chess Free App

The Chess King Learn app ratings are highly exaggerated. My max rating is 2242. And current rating is 1943. And in AI Factory's Chess Free app, my level is Level5 which is ELO 1352. Basically Chess King Learn course is very liberal.

CT Art 4 bought

I have bought CT Art 4.0 course from Chess King Learn. I was not clear on making better moves. I was making mistakes. I could not grasp the concepts from my earlier courses like elementary tactics and chess opening blunders. So yesterday I bought this digital learning material from Google Store. It cost me Rs.500.

Chess is interesting. And I want to learn this game. I play on tab.

With this course, I hope to learn systematically and improve my game.

Gamma expression ?

The expressions by Euler are presented below:

A Tall Building

Consider a tall building to be built.
To a normal man if ground floor takes 2 months to be made then 50 floors will take 100 months.
But as the number of floors increases the complexities increase. Because of height.
Is there anything in nature that can be used to help compute complex things like making a tall building. Or facing the challenges of career growth or financial growth or improving relationships or just parenting well.
The above are the challenges a human face. He looks to nature to solve his problems. And he looks to his own endeavour to solve his problems.
I believe in mathematics and its role in solving problems of humanity.
There are two approximate formulas and one 1,3,6,10,15 . . . series developed by me.
I have an intuition that the above will help in solving problems like making a tall building.

Approximate Formulas

Pulikachal and Rasam

Pulikachal is a famous dish made in south India. The main ingredients are tamarind and sesame oil. It can be mixed with rice and eaten. It can be eaten with chappatis too.

Rasam is also a famous dish made in south India. The main ingredients are tamarind and ghee. It can be eaten only with rice. However, sambar which is closely related to rasam can be eaten with chappatis. Because sambar contains dal (pulses or legumes).

Rasam needs water for preparation. The water gets about halved in cooking. For areas with water scarcity, pulikachal will be more suitable especially for rice eaters.

One contribution which our country will ever remember is the mid-day meal schemes of government for school going children. Now, they have included eggs too.

My chess rating is about 1700

I am poor in end games. I am little poor in significance of a move. But I have made a philosophy. This philosophy gives me confidence. However chess board pieces and moves confidence is less.

Overall I may have a philosophy. My rating about 1700. But chess like imagination is poor.

Chess rating now

The end game and making moves during middlegame are tough. I am making wrong moves and points are deducted.
My current rating is 1776. I reached 2140 and now its reduced.