What I mean is . . .

My favorite equations (and/or) I too have made it

My favorite expressions are down below. They are in the order I like. I do not have formal mathematics knowledge except "Engineering Mathematics". I learnt from Wikipedia all by myself. I had no books or guru to teach me.
The order and the equation:-
1. Niels Henrik Abel
2. Leonhard Euler
3. Carl Friedrich Gauss

You may recall that I too managed to make a set of equations. My rational series. Though they are hardly of great level but still there are two points that I wish to say:-
1. The polynomials are of two types. One involving (n+1)/(n+2) - (n-1)/n. And the other is n/(n+1) -(n-1)/n.
2. Apart from polynomials they can be roughly represented as geometric progression too till finite number of terms.
Here is the link to Rational Number Series and Polynomials.

If I can develop polynomials and geometric progression till finite terms reading only Wikipedia. Imagine what I can do if I get a formal training and chance to read books by great authors !! I would also like to remind that I have done "rough work" on Gauss too and have obtained approximate results. Then there are my #PythaShastri mantras.

Polynomials from the Rational Number Series

The rational number series gives exquisitely beautiful polynomials.
My mental prowess is less in making polynomials. I can make only the simple ones.So, I tried Wolfram Alpha. And it delivered the results.
I am attaching the snapshots of the polynomials. I am attaching 12 snapshots. Well, 3 of them gives golden ratio. n^2+n-1 terms.

India China tussle

India China tussle at Ladakh over border issue is very painful to read.
As a blogger I feel it is my duty to write my opinions on it.
Border means different thing to different people. When the British divided it was the British idea that mattered and most of the people obeyed.
But it is not British on the Ladakh side. India had rightly made Ladakh the union territory earlier.
But now there is a dispute.
India is the place where Gautama Buddha was born. I hope China respects the Buddhist philosophies and accepts peace. Hope the Chinese are "repelled" by India's respect for Buddha.

Two things I want to say

Firstly, I have obtained an equation for the Golden Ratio. This is indeed a big feat. This gives the golden ratio value accurately (unlike my previous blog post on golden ratio with agm logic).
Well, the equation that gives the golden ratio phi is the solution for n in
(((n+1)^2)/((n+2)^2)-((n-1)^2)/(n^2))/(((n+1)/(n+2)-(n-1)/n)^2)=0. This is from the rational number series. Actually the equation can be simplified to n^2+n-1=0.
Thus the golden ratio value as -1.6180339887. . . . . . . . .  is obtained.
Secondly, a prime number generator as effective as the Euler prime number generating polynomial is now made from the Rational number series.
The equation is
(((n+1)^2)/((n+2)^2)-((n-1)^2)/(n^2))/(((n+1)/(n+2)-(n-1)/n)^2)+42 generates prime numbers.
I have tested for 1 to 400. As much as 67% (268) of the results are prime.
Basically Euler prime generating formula was k^2-k+41. Mine is equivalent to k^2+k+41.
But both the above results can be obtained from the Rational number series. i.e the series
(((n+1)^2)/((n+2)^2)-((n-1)^2)/(n^2))/(((n+1)/(n+2)-(n-1)/n)^2).(equivalent to n^2+n-1)
So, the results are original.I feel privileged and feel honored to have got two of the finest results of mathematics. The Golden Ratio. And the Euler Prime Generating Polynomial.
Have great day!! Hope we all get freedom from the Covid-19 pandemic soon !!

This gives Golden Ratio phi to 10 places

The above formula gives Golden Ratio to 10 places. It gives 1.6180339887.

You may try this in your calculator and see. Using the Windows 7 calculator will be ideal.

I got agm(7,8,10) as 8.2878898435271

I got agm(1,2,3,4) as 2.3545004777747

You have to be careful with the brackets. 

You may observe that the above equation makes sense considerably. There is a geometric progression equation sort of too.

As the equation is of Golden Ratio, I thought of sharing it.