Happy New Year 2021

 Naya saal mubarak ho, hai meri pooja kai;

Yahi samay hai karne ka, nahin dooja koi.

Goodbye 2020

Goodbye 2020. Today is 31st December 2020.

Here's wishing a very happy 2021 with this expression.

Once again wishing all my blog readers a very happy new year 2021. I hope your wishes come true in the new year.

This is important

 

The expression 2n/((2n-1)(2n+1)) works both with three consecutive numbers and four consecutive numbers. Only thing is with three consecutive numbers it is equal with sigma for 1 to infinity. And with four consecutive numbers it is equal with integral for 1 to infinity.

Here are Wolfram Alpha screenshots

An equation in the last week of 2020

 Here is an equation in the last week of 2020. A similar equation was made earlier. I have added another variable m to what I did earlier.

Kindly check the equation for random values of m and n. Revert to me back if there is an error.

Have a nice week, dear readers !!

A Big Statement

A big statement from a man of limited learning. Forgive me if I am wrong. Consider me suitably if I am right.

I have extended what I had done earlier. See this and this.

Corrected expression as on 2021/03/04 is below:-

Planned journey of a self guru

Firstly, I hope the meeting between farmers and government meets success. The meeting is scheduled on Tuesday the December 29th. I urge both the government and farmers to focus on success of the meeting. That is both should prepare to give in.

Secondly, I wish my mathematical ambition gets a lift. My e, beta function and gamma function are strong. I have also given explanations on Fourier series and partial differential equations in my blog. So heat equations should be an achievable target. SAIL officials if are reading this, I request to give me a pull.

Thirdly, art drawing. I have made plans for 6 months. First three months I shall work on perspective and shading. After finishing to considerable improvement; I shall work on hands and folds in clothes. The next three months.

Three important thoughts

First thought

When we think of a number; we feel it should not be 0 or infinity. In other words G and 1/G should be valid statements. Another thing is Pythagoras law should be valid. In other words square root 2 and square root of cos(x) and sin(x) should be valid.

Gauss constant says that.

Second thought

The philosophy of pluses and minuses is true. In other words philosophy of the mathematical constant pi is true.

Third thought

Man indulges in counting 1,2,3 . . . However the mathematical constant e is true.

I have explained the philosophies of pi, e, G and earlier gamma (Euler - Mascheroni constant).

I hope you like these philosophies. In case you feel different, then please add comments. I will be waiting for your comments.

Till then have a great day. Hope you have a enjoyable week ahead. And a great new year after that.

An intuition proved right

About 4 years back a thought came in my mind. 1 to 2 is hundred percent rise. But 99 to 100 is just about one percent rise. Is there any "constant" for this I wondered.

I will explain it. Only today it became clearer.

Consider 1/1, 1/2, 1/3 and so on. It decreases considerably.

Now consider 1/2,2/3,3/4 and so on. It increases but not considerably.

If we take to the power of 1/2,2/3,3/4 and so on then the increase may be considerable.

So the "constant" I wrote in first paragraph is 1/n +log(n)-log(n+1) summed up for n from 1 to infinity. Isn't it?

Well that is what is Euler-Mascheroni constant. Gamma. 0.577. . . . .

How is this for beauty ? My master Euler it was. Amazingly beautiful !!

The Golden Ratio

Remember the post on strange things in infinite series. In case you have missed, here is the link.

Now, take a look at the image below.

This one is the third one on Golden Ratio.

Before this one there is one on Pentagon construction. And another one on agm(7,8,10)/agm(1,2,3,4).

And today is Indian Mathematics day. What a great thing !!

Today (22nd December) is Indian Mathematics Day

Today is Indian Mathematics Day. The birth anniversary of Srinivasa Ramanujan. He was born on December 22, 1887 in Erode, Tamil Nadu.

His major contributions include Ramanujan Tau Function, Ramanujan Theta Function. About these two I have written blog posts. He also has done work on continued fractions. And on nested radicals. And more. Basically these are the areas I am aware of. I think there are hundreds of areas he has touched and left mathematicians puzzled.

On this eve, I would like to present an expression of Pi. I do not think I have presented an exact equation like this earlier in my blog posts. 

Here is a Wolfram snapshot too.

Have a great day blog readers!!

The beautiful four

This idea came into my mind and I tried the expressions in Wolfram Alpha. I do not think I tried this idea earlier.

Many people who do not understand what I talk about I want to tell this.

The general expression which I try out is ((mn+m-1)/(mn+m) - (mn-1)/(mn)). Putting m equal to 1 gives n/(n+1)-(n-1)/n; three consecutive numbers. Putting m equal to 2 gives (2n+1)/(2n+2)-(2n-1)/(2n); four consecutive numbers.

My whole thing I had been focusing on for the last one year or so is summed up in above. This idea of ((mn+m-1)/(mn+m) - (mn-1)/(mn)) has been tried on finite sigma, infinite sigma, binomial, integral, complex function, Gauss etc. And it has fetched clear cut results. This implies ((mn+m-1)/(mn+m) - (mn-1)/(mn)) is a great function. I have published papers in JETIR and IJMTT.

Right now as I have written in the first paragraph, I tried my ideas more. And here is the result.

Why should I do it? Revelation of numbers in hour glass is the reason. I believe revelation by nature/God.

Have a nice day, dear readers !!

On RCEP and farm laws

 Kya kimat doge janaab gehoon ka ya jwaar ka;

Apni kimat ka pata nahin kya kahoon kuch aur ka.

Indian farmers have a mentality of above and they are right. It is difficult to bring farming under "Indian economy" as we know. 

Take my case. I am definitely good in mathematics. And what have these people in government done. Nothing. And "Indian economy" they talk of. You need to think of profitable moves dear. Not partisan moves. K K Birla used to say "Take care of small things ". How right he was !!

Instead of making India move towards RCEP the government is taking on its own farmers. And it is a pity. Farmers are loosing lives.

Open up the banking. Make it 100 percent transparent. We will then move towards RCEP. Then apply for membership. This is what India needs to do. And not farmers.

This is interesting

 

The above is so interesting.

If you take the sigma, the negative 1 term and n factorial common on the left hand side and add; basically n(2n -1) + n is 2n*n. Of course you cannot do this on infinite sigma. But the result on LHS is 2nsquared.

And the result on RHS is nsquared.

There is one on Ramanujan too. 1+2+3+4+ ........ upto infinity is -1/12. If you don't believe this, see Youtube.

Strange ways of infinity. Infinity is closer than you think. Just rotate about yourself and you are talking of infinity. And take a scale (however long) you are talking of finite.

Analysis of Infinite by Euler in two parts must be a great book. But then it is very costly and is unaffordable in general standard.

Have a great day, dear blog readers !!

Four expressions

 The below four expressions are one and the same.

1. The expression on the leftmost side are 4 numbers. (mn) and (mn-1); and (mn+m) and (mn+m-1).

2. The expression on second from left are numbers in arithmetic-geometric  progression.

3. The expression on third from left is factorials.

4. The expression on right is reciprocals/

Do you like it? Or do you dislike these type of posts? Do let me know.

If you dislike, I shall discontinue posting on these type of posts.

A new expression

I was thinking on an idea. My idea when expressed in terms of n seemed to be n/((n+1)^2) alternately negated and added.

I used Wolfram Alpha to know what the expression fetches.

Here is the result

And here is the Wolfram screenshot

Hope you like the expression.

Have a nice day dear blog readers.

Prime numbers generator

Euler, my master made a terrific prime number generator years ago. The formula was m*m-m+41.

I thought m*m+m+1 was a great prime number generator. This was two years back when I wrote the paper on "Rational Number Series". Then I followed Euler somewhat and made it m*m+m+41. Also I tried m*m+m+2657.

With m*m+m+1, 311 prime numbers are generated for m equal to 1 to 1000.

With m*m+m+41, 580 prime numbers are generated for m equal to 1 to 1000.

With m*m+m+2657, 498 prime numbers are generated for m equal to 1 to 1000.

Here are the snapshots of the results.

Special thanks to onlinegdb.com for the C compiler.

My point in writing this article is this. Euler was so great. It was 17th century. Still he managed to get the magical number of 41. 

If you are curious how 2657; well it is nearest odd integer to 16.3 into 163. 163 being a favorite number of Ramanujan.

I think we can go ahead and try with nearest odd integer to 1.1 into 11, 1.9 into 19, 4.3 into 43 or 6.7 into 67.  Please try these if you are stuck up wondering what to do during COVID.

Have a nice day, dear blog readers. And in case you can beat by generating more prime numbers; do let me know.