I believe that I am getting the feel of Euler-Mascheroni constant. However my expressions are not strong.
This finishes my mathematical endeavours.
Friday, August 30, 2019
Tuesday, August 27, 2019
The sixth Rational Series expansion
I had made five Rational Series expansions. These were:-
1. n/(n+1) - (n-1)/n = 1/n = 1/(n+1)+1/(n+1)²+1/(n+1)³+1/(n+1)⁴+ . . . . . .
2. The sequence n/(n+1) - (n-2)/(n-1) and the connection this series had with triangle series. The growth of this series was like 1/(4 * triangle series term).
3. The numerator i.e (n - √(n+1)*√(n+1)) of the expression √n/√(n+1) -√(n+1)/√n was approximately 1/(2*n)
4. n²/(n+1)² - (n-1)²/n² is approximately 2/(n+1)²
5. n²/(n+1)² - (n-2)²/(n-1)² is approximately prime / (n*4)². This was the prime number generator and more than 30% of the results were prime.
Today, I made the sixth expression. And that is
6. √ n/√ (n+1) - √ (n-2)/√ (n-1) is approximately 1/n².
So six expressions have been made. It may be confusing for a normal reader of my blogs. But these may be important. I have called then # expressions.
I am able to better my rational series expressions to be more accurate. However Euler totient functions exists. Euler totient functions are better expressions than rational series expressions. I have no doubts about it.
More accurate rational expressions are:-
1. The numerator i.e (n - √(n+1)*√(n+1)) of the expression √n/√(n+1) -√(n-1)/√n is more accurately 1/(2*n) + 1/(8*(n+1)³)
2. n²/(n+1)² - (n-1)²/n² is more accurately 2/(n+1)² + 1/(n+1)⁴
3. √ n/√ (n+1) - √ (n-2)/√ (n-1) is more accurately 1/n² + 1/(2.n³).
This finishes my mathematical endeavors.
1. n/(n+1) - (n-1)/n = 1/n = 1/(n+1)+1/(n+1)²+1/(n+1)³+1/(n+1)⁴+ . . . . . .
2. The sequence n/(n+1) - (n-2)/(n-1) and the connection this series had with triangle series. The growth of this series was like 1/(4 * triangle series term).
3. The numerator i.e (n - √(n+1)*√(n+1)) of the expression √n/√(n+1) -√(n+1)/√n was approximately 1/(2*n)
4. n²/(n+1)² - (n-1)²/n² is approximately 2/(n+1)²
5. n²/(n+1)² - (n-2)²/(n-1)² is approximately prime / (n*4)². This was the prime number generator and more than 30% of the results were prime.
Today, I made the sixth expression. And that is
6. √ n/√ (n+1) - √ (n-2)/√ (n-1) is approximately 1/n².
So six expressions have been made. It may be confusing for a normal reader of my blogs. But these may be important. I have called then # expressions.
I am able to better my rational series expressions to be more accurate. However Euler totient functions exists. Euler totient functions are better expressions than rational series expressions. I have no doubts about it.
More accurate rational expressions are:-
1. The numerator i.e (n - √(n+1)*√(n+1)) of the expression √n/√(n+1) -√(n-1)/√n is more accurately 1/(2*n) + 1/(8*(n+1)³)
2. n²/(n+1)² - (n-1)²/n² is more accurately 2/(n+1)² + 1/(n+1)⁴
3. √ n/√ (n+1) - √ (n-2)/√ (n-1) is more accurately 1/n² + 1/(2.n³).
This finishes my mathematical endeavors.
Saturday, August 24, 2019
My Zen in mathematics
I have got peace in mathematics.
Well mathematics is not similar to engineering and technology. In the sense that Euler did not copy Maclaurin to get the sine, cosine series in his e to the power (i theta). In engineering a gear box idea may be a patent. But in mathematics it is not. It is nature.
So rediscoveries were not affecting me. What was affecting me was the quality and quantity of my ideas. I used to think I am only 10% of the greats in mathematics.
But then yesterday a thought came that though my quality and quantity are less; the fact cannot be denied that my ideas came from a single stream of thought. The golden ratio.
This gave me my Zen. My peace.
Best wishes to my blog readers.
Well mathematics is not similar to engineering and technology. In the sense that Euler did not copy Maclaurin to get the sine, cosine series in his e to the power (i theta). In engineering a gear box idea may be a patent. But in mathematics it is not. It is nature.
So rediscoveries were not affecting me. What was affecting me was the quality and quantity of my ideas. I used to think I am only 10% of the greats in mathematics.
But then yesterday a thought came that though my quality and quantity are less; the fact cannot be denied that my ideas came from a single stream of thought. The golden ratio.
This gave me my Zen. My peace.
Best wishes to my blog readers.
Monday, August 19, 2019
Salem Steel Plant privatisation
 |
| Make in India lion made with Salem stainless steel |
SSP produces high quality stainless steel. It is known in every house in India.
SSP can take on competition from Tata and Jindal.
SSP is dependent on its market and trusted financers for its running. It is not a loss making firm in the long run.
If a boost is given by the government of India, SSP can make profits.
Privatisation may create job losses of many in SSP. This is undesirable and may cause unrest.
Nicotine Addiction
Earlier I used to smoke cigarettes. I was addicted to cigarettes.
But later I tried nicotine chewing gum to stop smoking. It did not work out.
When I came to Ranchi, I was into smoking and nicotine chewing gums. Then an idea cropped up. I replaced nicotine chewing gum (which was very costly) with khaini in small quantities.
Now I have stopped cigarettes completely. Only khaini. A packet of khaini of Rs5 lasts 2-3 days. I think addiction is less.
But later I tried nicotine chewing gum to stop smoking. It did not work out.
When I came to Ranchi, I was into smoking and nicotine chewing gums. Then an idea cropped up. I replaced nicotine chewing gum (which was very costly) with khaini in small quantities.
Now I have stopped cigarettes completely. Only khaini. A packet of khaini of Rs5 lasts 2-3 days. I think addiction is less.
Sunday, August 18, 2019
Thought fights
I don't like thought fights. I don't indulge in thought fights too.
It is impossible to try and beat a Gauss idea. Or an Euler idea. Or a Maclaurin idea. Or a Fourier idea. Or a Reimann idea. Or a Taylor idea.
I wrote about Laurent series because in my blogs elsewhere I had written on
1. Poochi system
2. Complex conjugates and examples
3. Power series of complex numbers and examples.
I am not very interested in engineering entrance exams or in the courses taught in Indian institutes of repute.
Only guilt that affects me is that I could not make it like Ambanis. Seriously. I always think that I should contribute financially like Mukesh or Anil Ambani.
Another thing that affects me is the military. And I am defensive. Not offensive.
So time, periodicity are tough for me.
But I think I can explain. Wait for my blog post on this.
It is impossible to try and beat a Gauss idea. Or an Euler idea. Or a Maclaurin idea. Or a Fourier idea. Or a Reimann idea. Or a Taylor idea.
I wrote about Laurent series because in my blogs elsewhere I had written on
1. Poochi system
2. Complex conjugates and examples
3. Power series of complex numbers and examples.
I am not very interested in engineering entrance exams or in the courses taught in Indian institutes of repute.
Only guilt that affects me is that I could not make it like Ambanis. Seriously. I always think that I should contribute financially like Mukesh or Anil Ambani.
Another thing that affects me is the military. And I am defensive. Not offensive.
So time, periodicity are tough for me.
But I think I can explain. Wait for my blog post on this.
Thursday, August 1, 2019
These are important
A number n progressive is an important thought of a man.
So is the number n squared progressive.
Also a human wonders about combinations and factorials as the number n progresses. n!.
The + and - signs is an important element in human thoughts.
So two expressions, I present below. They are very beautiful indeed.
So is the number n squared progressive.
Also a human wonders about combinations and factorials as the number n progresses. n!.
The + and - signs is an important element in human thoughts.
So two expressions, I present below. They are very beautiful indeed.
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