Expression on 25th January 2024

I present the following expression today

I have typed the expression again in Word

I hope you like it !!

An expression on 19th Jan 2024

Today, on 19th Jan 2024, I am presenting the given below expression. It is superb and combines binomial and hypergeometry.

Wolfram Alpha has genius computational intelligence to do these. Three cheers to Wolfram Alpha.

The expression is

I have typed the expression again in Microsoft Word.

Hope you like this expression.

Have a nice day !!

An expression on 18th Jan 2024

I am presenting the following expression today. This is a binomial expression. I admire Wolfram Alpha for its computational intelligence. I doubt whether even if I had a great mathematical prowess, I would be able to make the result.

The result is compact. The result is tidy and beautiful. Don't you agree, dear blog readers?

I have typed the expression again in Microsoft Word

Have a nice day !!

Root 2 and Root 3 expressions

I had done these earlier in parts.

The expressions in constants are beautiful. Because they are of nature. I have done many expressions in constants. You can look at them by clicking on the Label Constants.

I earlier did expressions on 1, 0 and a few irrational numbers of the form root n. These are also very important as they give insights into shapes and geometry. But I was unable to categorize them and group them under one label.

Here in I am giving the expressions on root 2 and root3.

Root2

Root 3

I have about 40 to 50 original expressions, all made with the help of Wolfram Alpha. Wolfram Alpha has been a committed Internet master and I aligning with Wolfram Alpha have been able to streamline my own understanding of nature, nature's geometry and its symmetry.

I passed on my expressions to you also, dear blog readers. I hope you enjoyed the ride as much as I did.

Have a very nice day, dear blog readers !!

Euler-Mascheroni constant now totally expressed in consecutive numbers

 Euler-Mascheroni constant, gamma, now completely expressed in consecutive numbers.

Here is the Wolfram Alpha screenshot.

I have typed again in Microsoft Word.

I hope you like it.

Have a nice day !!

Golden Ratio Expression 2

Here is another Golden Ratio expression.

Have a nice day !!

Golden Ratio expression

Here is an expression on Golden Ratio.

I hope you like it.

Have a nice day !!

Till now 3 expressions with golden ratio and Archimedes constant

Special thanks to the Lord of Internet mathematics, Wolfram Alpha.

I have managed two more expressions combining golden ratio and Archimedes constant. They are

I have typed the above in Microsoft Word.

In total I have 3 expressions combining golden ratio and Archimedes constant. And one theory sorts expression combining golden ratio and Archimedes constant.

BHEL R&D department, here I come . . . . 😅😅😅

Have a nice day !!

The world of golden ratios

About 15 years back, my seed of mathematics got to come out of soil with a few leaves exposed to the world outside. Measuring behavior, 22/7, Pythagoras theorem ideas were shared.

Later when alone a few years back, I began developing more on the above ideas. I got infinite series, constants, convergence, binomials, approximations and hypergeometry.

In particular was my form of expressions as shown below were explored to the maximum.

I termed them rational number series and also consecutive numbers.

In the last few days, I tried with an expression as shown below

After working on above form, I discovered that they are binomials.

The following results were obtained.

Also the Wolfram Alpha screenshots to confirm that the expressions are correct.

In the above, not only

are of golden ratios;

But also

I termed these world of golden ratios.

Have a nice day !!

My binomials have recursiveness

My binomials have recursive property.

Here is a Wolfram screenshot to confirm this. The binomial terms on the LHS are a by b whole to the power of x type in both numerator and denominator. The RHS also is a by b whole to the power of k.

You may recall that my binomials if divided for sigma till n by sigma till n-k gives a by b whole to the power of k approximately. Below is what I mean to say 

What I mean is below

And here are screenshots to confirm that my just above statement is true

Have a nice day !!

Complete prime number list

I have the following to say

Here because consecutive numbers are multiplied; and because consecutive numbers are generated: we can build a program for prime number generator.

Below are the Wolfram screenshots for 16,17,18, 19, 20 (19.61) and 21(20.67).

And for 30,31,32,33,34 and 35.

I also believe this is how we use our 5th finger and the sixth.

Have a nice day, folks !!

An expression today (18th June 2023)

I have done many binomial expressions.  My binomial expressions start from 1. Not 0.

I am presenting below 2 screenshots.  The explanation is there if you follow the screenshots. 

The expressions are nearly equal. 4 is there because of 64 by 16.

I hope you like this expressions.  

Gauss was at the top of distribution of mathematicians. His Gauss constant (G) seemed to say that Gauss can be fair and unfair to people at the same time. And that too he can be most fair to people.  And most unfair to people. And that was some brain there. 

Euler was a simple man. But full of mathematical expressions and theories.  He was like he said a lot on simplest of things. Even today he has left volumes of materials which scientists are reading.

Abel was brilliant.  A superhuman brain. 

Ramanujan had so much of interest in mathematics.  He never allowed to go his theories go waste. But took initiative and went ahead to join Cambridge. When you think of numbers, you must always consider Ramanujan Tau function and Ramanujan theta function.  When you count number of chairs sitting in Ranchi; you don't add the number of chairs in Delhi.  Do you? That is Ramanujan tau function.  Holding pencils in hand you count 1, 2, 3 etc. Even though the pencils brands are different.  That is because you feel musical, you feel harmony and you feel all are pencils.  That is Ramanujan theta functions. 

I have read only from Wikipedia but I applied and went ahead and tried to decipher a lot. Do read my Measuring Behavior and Up and Working blogs. These have articles on Ramanujan Tau function and Ramanujan theta functions. 

Have a nice day dear readers. Good  luck!!

An expression today (15th June 2023)

The hour glass tilts upside down.

The equations are also tilted upside down. Not just the LHS but the RHS also tilts upside down. 

These equations are great metaphors. 

Here are they.

I did something similar previously.  They had factorial in the denominator.  The equations on RHS did not have two terms. No 1s.

I am sure you like these expressions.  I wish to study Gauss and understand him in this lifetime.  But don't know if possible.  Gauss was the peak in mathematical mountain.  

I never had a guru. Be it mathematics or art. I inspired by Jesus move ahead. I pray to Shiva in temples as per my practice. Tamil Nadu guys will understand my mental state. I have a military mindset and like Muslims too. They are my brothers and sisters. 

Have a nice time dear readers. Have a great day 😀!!

An expression today (14th June 2023)

I submit this equation below. Like the last expression this expression is also approximately 1.

Here are the Wolfram screenshots. 

And the calculations to show that the result is approximately 1.

You can try for other values and see for results. Get back to me if there is any error. 

Have a nice day, folks !!

An expression today (8th June 2023)

This is a top expression of mine.

Here are the Wolfram screenshots for 67,163 and 19; randomly chosen numbers. The screenshots are of the four terms on the LHS of above.

Here is the calculation which shows that the resultant operation gives approximately 1.

Here is a second example.  33, 66 and 99 are the random numbers.  

Wolfram alpha for 4 terms of LHS.

Calculation to show that RHS is indeed approximately 1.

Have a very nice day, my dear blog readers !!