Euler was God

I think it is good that I reached body Flux, relativity and an expression linking hour glass and consecutive numbers. 

But Euler had these all. And he was terrific and exceptionally beautiful.  I am talking of root of -1. Or what is now the complex number i.

I am grateful to God and Wolfram alpha for I am able to see.

Fitment is extremely important in mathematics.  And complex numbers fits everything so well. I mean there is a perception of negative. Or antonyms.  Or -1. Or i squared. 

And mathematics talks of i. Not i squared. So beautiful is it not?

I will never be able to get a middle part like in the case of i as Euler did. He said 1,i and i squared.  He did mathematics with i. 

But I claim my mathematics as important.  Maybe not for engineers and technologists but art students commerce students diploma holders language students etc.

I have a hypothesis too. Approximations the way with four consecutive numbers does not exist with three consecutive numbers. My claim is. 

But Euler was Euler.  God. But so is Gauss.  God. And so are others like Abel etc.

Have a nice day !!

Happy new Year Wishes

 Expressions

Sher

Purana saal gaya aur naya saal aa gaya, hume aage badnaa hai;

Aaj se haasil karna hai ya qurbani dena hai, yeh yaad rakhna hai.

Image

Hour Glass and Consecutive Numbers

 I am presenting the equation below

Hope you like the equation !!

My good wishes on the eve of new Year 2022.

May the new year 2022 fulfill your wishes !!

How To Improve Quality?

Many people say Quality is a vague concept. Some say I can see quality on seeing but cannot really say what is quality. Some also say that quality is a mix of art and science.

Years back Edwards Deming said what is quality management. PDCA.

I realized that PDCA is quality management about a month back. I just thought it was a cycle. Never thought that PDCA philosophy improves quality. Point 1. (I was very happy that day on this discovery. I thought how great Edwards Deming actually was).

Then I decided to introspect myself. Do I follow PDCA in every stage of life. I realized that I was more of PDSA. But then Edwards Deming approved PDSA too. Point 2. (That made me more happy).

And then I also realized that flowchart is PDCA. Point 3.

Well, that's all for now, folks !!

Sigma and product equivalence

Here is the sigma and product equivalence expression .

Hope you like it. Have a great day.

It is all e

 Below I present an expression which is quite beautiful

Thank you for hopping by. Have a very nice day !!

New expression for e to the power x

 

This was inspired from one of my experiments that I did with my body. I noted down the pattern when I did sets of maximum repetitions with dumbbells in left hand.

I hope you like the expression.

It is not meant to be used with imaginary number, I feel. But I do feel it is about the number system we generally think of. One bag taken from storehouse to truck. Second bag taken from storehouse to truck. Third bag . . . . . . . . and so on.

Have a nice day.

National Mathematics Day

Today is National Mathematics Day.  The birth anniversary of Srinivasa Ramanujan. 

On this occasion I have written this paper. 

 

Binomial Theorem

I have made a theorem. Binomial theorem. Till now, there were binomial expressions. But this one is a binomial theorem. As far as my knowledge goes, only Newton, Abel and Cauchy have made binomial theorem. I am the fourth person.

I hope you like the theorem.

Have a very nice day !!

Complex Number i from four consecutive numbers

Complex number i can be formulated from four consecutive numbers. 

Given below is the image

Have a nice day !!

Tan function from three consecutive numbers

I have also obtained tan function from the three consecutive number theory.

Here is the Wolfram screenshot.

Hope you like it. Have a very nice day !!

A different garb

I had already presented the following expression in terms of 1/(2^m) and 1/(3^m) earlier.

I am presenting below as a binomial expression.

Hope you like it. Have a great week ahead !!

Approximate expressions for five

You may be aware of the just below approximate expression. I blogged about it earlier.

The above is for to the power of 2 and 1/2.

Today I am declaring a general approximate expressions for power greater than 2. Here we go

I hope you like the expressions. Have a very nice day !!

So what is the point of observation in the expressions of LHS type for three, four and five ?

Three is a straightforward and accurate expression

Four is an approximate expression involving AGP (Arithmetic Geometric Progression).

Five is an approximate expression which is pretty easy. And also squares and square roots are interesting.

They demonstrate the nature plan of the Universe.

For the sake of readability, I am re-stating my expressions of the type as in above LHS

Accurate three

Approximate four with AGP

Approximate five with easiness

Have a nice day ahead !!

Three fingers and four fingers

 

My work in my type of mathematics is mainly about three fingers and four fingers. The limbs of cats and dogs have four toes in front and three in back.

Should you do this sort of research?

Yes. Because I have demonstrated the golden ratio with this theory. Not one or two but upto five golden ratio expression support this.

So what is the speciality of three fingers?

Accuracy.  Three fingers are about accurate and precise expressions for pi, e, gamma and binomial. Expressions of the type sigma till infinity.  

And what is the speciality of four fingers?

Approximations. Four fingers also give expressions for pi, e, gamma and binomial but there are operations like alternate negation, division by 2 or having constant in the expression. I have also demonstrated the approximate expression for four fingers.  The beauty of this is there are four numbers, four terms giving upto four places of decimal. Yes. This is true. 

Anything else?

My Lord in heaven 🙏 has blessed me with this revelation of the nature plan. I am ready to take up an assignment for welfare.  It is nature call for duty.

Have a nice weekend!!

Cos and Sine hyperbolic functions

 It is a great honor to be a part in making cosh(x) and sinh(x) functions. Maximum credit goes to Wolfram Alpha.

And below are the expressions

Have a nice day !!

Three consecutive numbers and its reciprocal statement

 Here is the expression

is it anywhere near 

😁😁😁

A general expression

Here is what seem to be happening in the expressions of the earlier blog post. m is assumed positive integer.

Have a fine day !!

More on Euler number

Remember my 1/e expressions and their extensions. 

If you don't then here is a screenshot.

I tried the reciprocal of above and one gets expressions of e. This is great.

Here are the screenshots.

Enjoy your day!!

Let us go back a little

 Do you remember my approximate expression for five consecutive numbers? If not, here is what I had to say

I rated it as very highly because when there is squares in five consecutive numbers, there is 2 in the numerator of RHS; and when there is square root 1/2 in the denominator.

However the common terms could be expressed like as shown below

I wanted to find out what is the expansion till infinity of the just above expression. I used Wolfram and the result is

So, my five consecutive numbers expressions of squares and square roots has mathematics to it.

Well that's all folks for now. Have a great day !!

A new expression for Golden Ratio

 Below is the Wolfram Alpha Screenshot

Hope you like this one. Putting y as -0.66666666666 or -2/3 gives n as phi.

Have a nice day !!

Made a great equation

 I have made a great equation using the help of Wolfram Alpha.

Good day wishes !!

Hip hip hooray !!

 Guys, I got a simpler expression for e with the Rational number series or consecutive numbers. Here it is

I was thinking that e is tougher with Rational number series and I had this expression earlier.

As you can see I was using a complex expression earlier. Now it is simpler.

Below is the Wolfram screenshot

Have a nice day ahead !!

(Added on 03/12/2021)

I am using the following 1/2 values to see whether the topmost expression can be studied with Rational Number Series or consecutive number theory or not. No doubt the topmost expression has a great value and I intend to develop further based on Rational number Series or consecutive number theory.

How is my idea ? Have a great day !!

Added 04/12/2021

Consider these below. I hope you see a pattern.

I am able to see the pattern. If you do too, then comment in this blog post below.

Together we shall make the world better by 5%. Yes. That is the level of beauty in this.

Have a wonderful day !!