Another Indigenous golden ratio transform

Here is another indigenous golden ratio transform.

minus m squared plus m plus one when equated to zero gives the golden ratio.

Hope you have a nice day !!

Indigenous golden ratio transform

My earlier blog post was a golden ratio transform. But it was not fully indigenous.  It had an expression of e^m which was borrowed from foreigners.

As I had e^m indigenous expression,  I decided to make changes in the formula.

Now here is the golden ratio transform. 

It is indeed indigenous.  All the subset expression are mine and the golden ratio transform is indigenous. 

Thank you Wolfram alpha.  You have been wonderful ❤️!!

Golden ratio transform

I have got what I have been dreaming about. An infinite series expressions which fetches the golden ratio equation.

First of all my thanks to Wolfram alpha.  You have taught me how to express.

Here is the golden ratio transform expressions. 

m squared plus m minus one when equated to zero gives golden ratio. 

Have a nice day!!

Width experiment

You may be aware that I have done three experiments with my fingers and hand.

One was lifting dumbbell with left hand. It helped me get an expression for 1 and new expression for e to the power x.

Second one was lifting dumbbell with right hand. It helped me with expression of 2. The most difficult. 

Third one was lifting okras with left hand fingers. This helped me in understanding gamma function.  And because gamma functions were termed equivalent to beta functions it improved my knowledge tremendously. 

Today I did the fourth experiment. 

Measuring width of an object with finger width. 

Distance            No. Of fingers

1 full distance        1 finger width

1/2 distance             2 finger width

1/4 distance             3 finger width 

The third reading was surprising.  I thought it will be 4 finger width but surprisingly it was 3 finger width. 

So 1 by m to the power of n of distance.  And n is the number of fingers.

Simple experiment.  But far reaching learning.

On Golden Ratio

Golden ratio is a seeing constant.  It is present in nature. But needs to be seen.

Here are four screenshots which exhibit Golden ratio equations.

You may be aware that I have three infinite series expressions of golden ratio. 

I also have support of 10 golden ratio expressions for my 3 to 4 consecutive numbers theory. 

Great Expression

Mixing the two expressions from my earlier two blog posts, one can get

You may note that we are dealing with infinite series here. (-n) and (-n+1) follow one another in one step. And combination (n,n-1) and combination (n+1,n) too. So that is the beauty here. And the result is 1.

You may know that e to the power of i into theta has similar properties. cos theta and sine theta follow one another. But the phase difference is 90 degrees.  Step of i to the power n.

Complex numbers are not just a+ib sorts. That is just the beginning. Electrical engineering supports this because magnetism and electricity have a 90 degree phase difference. i.

So complex numbers are much more complex than you would have learnt. Riemann zeta function, Dirichlet beta functions are functions dealing with complex numbers and they have a simple form which is suitable to numbers and number theory.

Did you learn something useful here ?

Another expression on 26-05-2022

The following expression was made possible entirely due to Wolfram Alpha. I am not taking credit for this.

Hope you like it.

Have a nice day !!

Expression on 26-May-2022

 I present the following expression today

Hope you like it.

Have a nice day !!

Conquered the numbers

This formula below can fetch (m-1) and in other words any number you wish to imagine. From zero to any. All in numerator. Not 1 by n. But n.

Here is the screenshot. 

Hope you like the expression. 

Have a nice day!!

Expressions of zero

I feel there is nothing called numbers. Humans used fingers. And numbers originated. And because human used fingers my consecutive numbers theory is fetching results on constants. 

But Ramanujan had a different idea on numbers.  He said zero is the origin of numbers.  He was a God of mathematics and he showed us the way.

Anyways. 

Here are three screenshots on expressions giving zeros.

I hope you like them.

Have a nice day!!

Perfection enough?

Perfect 

My art

Perfection

Perfect 

My art

I have potential.  Just need company.  

Four claims

 I make four claims. On being approximate enough. Accuracy is not an Indian viewpoint. But approximation is.

I want to claim my place on my merits, if possible.

Three strong intuitions

 Intuition 1

Intuition 2

Convergence theory which I term star-delta starter

Intuition 3

Support of as much as 10 golden ratio expressions for my 3 to 4 consecutive number theory.

These are what I will spend my thinking on. 

If possible I shall buy Gauss books.

Rare expressions

I present the following two expressions. One gives approximately a squared number and the other approximately a triangular number.

I hope you like the expressions.

Have a nice day !!

These results are already blogged about by me.

So in the just above if we increase k by 1 ( k is large) then the two results (with k and k plus 1) when divided give n squared in the first case and 2 n squared plus n in the second.

Essentially with the binomial in the RHS do the following operation

Put k as say 1000. Do the binomial sigma.

Then put k as 1001. Do the binomial sigma.

If we divide, then we get n squared in the first case and 2 n squared plus n in the second.

Is it not interesting?

Is it true for all functions?

Yes, it seems so.

So, the following seems to be the case. 

Here is a workout on Wolfram Alpha to support my just above statement

The result by dividing above two is 3. And 3 is what the function of n all about.

Symmetric expressions

 The following four are symmetric expressions

Hope you like them.

Have a nice day !!

This expression on 17-05-2022

 I present the following four finite expressions today.

                                        

Hope you like them.

Have a nice day !!

A knock at the doors of Sylvester medal

I dream of a knock at the doors of Sylvester medal.

Here is what. I believe. 

One percent chance on better sports ability

 Here is another expression which fetches 2^k binomial form.

So a lot many 2^k equivalent expressions. But in infinite series.

Infinite series are nothing great. To me it means always there. To mathematicians it is convergence. 

But one thing is certain. There is one percent chance that better sports ability can result with these expressions. Modi sarkar, ab to kuch karo kam se kam.

Let us move ahead. You, me and everyone. Let the government mechanism assist betterment.

It is high time.

Wishing you a nice day ahead !!

This expression on 12-05-2022

 I am presenting this expression today (12-May-2022, India time). This is another binomial expression of 2^k types. This is the fourth binomial expression of the type 2^k.

Newton made just one binomial expression of the type 2^k using (1+n)^k binomial expression. But Sir Isaac Newton made a finite series. All the four binomial expressions of the type 2^k of mine are infinite series. So if Newton gets 100 percent marks, I get 85 percent marks. But you need to know one opinion on Newton. Stephen Hawking had a dislike for Newton. This point is very important. So, should you have respect for Newton is the question.

Of course, my sincere thanks to Wolfram Alpha for making this expression possible.

Have a very nice day, dear readers !!

Indigenous Binomial Formula

Indigenous is the mantra of India, since India became a Republic. In this regard I made an indigenous cosine formula. Here is the link

I have made practical contributions too for India's indigenous objective. In music. I am talking of dafli playing and music scale.

Below I submit another indigenous formula. This time for the binomial 2^k.

This formula is very important and will improve sports performance, improve lifestyle by better acceleration of mindset, removing laziness from its roots and other benefits.

Two indigenous formulas one on cosine and one on 2^k made. Let us move on by 'Make in India' method.

This expression on 11-05-2022

 I am presenting the following two expressions on 11-May-2022.

These two are not exactly consecutive numbers. But I term them hour glass consecutive numbers. And the term is so apt like an English definition. Because the three consecutive hour glass expression gives zero. And the four consecutive hour glass expression gives -(1/2^k).

Amazingly beautiful. Made possible by Wolfram Alpha.

Have a nice day !! Enjoy your day !!