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Complete golden ratio formula for advanced KAAL number

KAAL number is 4.4.

Presently, 

is showing reasonably good results. 

You may recall 1+1/x+1/(x^2)=2 is the golden ratio expression. 

Then I said if we raise 1 to very small number, 2 to very small number and 3 to small number,  one gets LHS of just above expression. 

I was talking of raising only the n to some power. Say raising n to q/r.

What if we raise n to q/r, x to n+s/t and start from u/v and end at w/x. Is there an algorithm for this ?

Yes. Wolfram alpha is showing results. 

This can give advanced results for KAAL number.

But it is not in my hands. A big research team is required. 

Will this idea get materialized?

No. Because it is India. 

These two expressions give hope

KAAL number expressions were made. We used 1+2/x+3/(x^2) for p and got 1/2 number positions correct with correctly placed leading 0s.

The following two results from Wolfram Alpha are promising and we may get 2/3 number positions correct with correctly placed leading 0s.

I can check only a little with calculator and Wolfram Alpha. But I shall try.

But real thing is getting a nod from Professors of Mathematics.

My dreams of p of KAAL number

The present p

My dream of expressing p

Seems okayish

Advanced KAAL number theory is a problem. 

The value of p as below gives 2/1 numbers with 0s ahead correct.

But what if we need 3/2 numbers with 0s ahead correct.

The following helps.

You may note that the seed number is 227. And 227 is related to 772 as 1000 minus 772 is 227. And we are using 1.079 and 1.79.

What I mean in nutshell is that further scope in KAAL number exists. If. only I get a chance.  Only exam qualified guys get access to big computers. Not me. 

Few more infinite series to help find the right p1 and p2

 

Currently we are using the same p for 4.4^p/x and one(x)+pzero(x). This gives us first two digits correctly placed with the trailing 0s correct.

Maybe the above will help in separating p and making them p1 and p2, 

Whether e^ix or 4.4^p/x ?

I asked Google AI the question?

The answer

Completed for 227

 

Doubts in complex number i

Is not the i different in e^ix, cos(x)+i sin(x) and cos(x)+sin(ix) ?

Before touching my KAAL number it is advised that one gets clarity in above.

KAAL number stands for (Kirtivasan,  Abhaya,  Akshaya,  Lata).

Do. not work on KAAL number.  First work on clarity of i.

The 4 Ps

In mathematics,  I plan to keep 4.4 same for all but wanting p1 and p2 for the two expressions.  This I believe is nature's laws. While my readers want change in 4.4 itself. 

Now I am concentrating on art. Left mathematics with the above thing in hold.

I shall be concentrating on Perspectives,  Proportions,  Planes and Perpendiculars. The 4 Ps. The 4Ps will be aimed for with DMAIC and PDCA in mind.

I aim to draw like Terada Katsuya, but for comic drawing.  His book has arrived. 

Thanks for the book. 

Questions on the factor p

What is the factor p ?

The factor p is like i in e^ix =cos(x)+isin(x). It is 4.4^p/x=one(x)+pzero(x)

What is the current expression for p?

Is there scope in further improvement to p value ?

These two expressions throw a huge light on getting accepted p values. The two Wolfram Alpha screenshots are

By changing four parameters namely o, m, p and q we can get the required value of p.

So changing o,m,p and q to get required p should be easy. Is it not ?

No. It is in fact very difficult.  Supercomputer help will be needed. Six things have to be checked. 4.4^p/x, one(x)+pzero(x), o, m,p and q. It is a gigantic task and needs multiple processes. 

Do you have access to large mathematical computers?

No I have access to only PC and laptop. 

How do you plan to get access to large mathematical computers?

Interest in this theory by eminent mathematicians and pulling power of politicians can only help me.

Thanks. 

Thanks. 

Let's work on this for 4.4 number

The step for advanced KAAL number theory is changing the expressions of p.

Consider this result from Wolfram Alpha. 

And the results for seed number 227.

But the reality is not easy. Mathematicians of India need to make definitions. Remember how i was developed by 17th century Europeans.  Euler only talked of square root of minus 1. By consensus i came up. Indian mathematicians have to define p. Then after defining p Indian mathematicians need to do Indian gamma function.  And the third thing Indian mathematicians need to do is work on log equivalent of 4.4.

So much of hard work.  So much of coordination.  

Push and pull from India's topmost power centre is essential. 

But things seem feasible.  Things seems a golden ratio touch to number systems. 

I on personal level is in touch with mathematicians of a premier institute.

Advanced KAAL number theory development

 I plan to do my own research in advanced KAAL number theory development. KAAL number stands for (Kirtivasan, Abhaya, Akshaya, Lata) number.

The advanced KAAL number theory development is not changing 4.4 to something else. It is not changing the basic formula structures. It is not changing any structure of one(x) or zero(x) . But advanced KAAL number theory is about changing the p structure.

You may recall p from below.

Interesting results are there when we treat p as an infinite series. There are three results which are interesting.

The second one is what is the present p from.1/x^0 plus 2/x^1 plus 3/x^2.

Have a nice weekend, folks !!

And Finally

From 2024, I was mad with KAAL number. I was interested in approximate formula for (2n)! and I went to greater heights to know a mathematical truth.

I worked with Wolfram Alpha and kept moving onwards. KAAL number theory kept my mind occupied more than pi, phi, binomials and combination(2n,n). I kept moving ahead.

I would like to state here that KAAL number theory is due to an experiment. An observation. You may be aware that I have done experiments in Number Theory and in this blog I have made an Experiments tag too.

I expected help from mathematicians. Help from Institutes. But I was rejected .

In this blog post I am stating my FINAL KAAL number results.

The gamma function is actually an e function. Just changed it to suit 4.4.

Have a nice weekend guys !!

Spending time

You may be aware that I stay in Ranchi with my mother. And I have 4 hours time with me. Daily. 

I spent time in expressions with Wolfram Alpha.  But not anymore.  Because expressions have dried up.

I now plan to spend time on drawing on digital. Drawing practices on paper. Harmonium. 

Hope Lord Jesus helps me in spending time thus.

Have a nice day!!

Approximate gamma values

 

And Wolfram screenshots to confirm the correctness

I wanted to build Indian gamma function. But my KAAL number gave only approximate results. But here in I am able to show approximate gamma function. This is truly a very happy day for me. Mathematics is not my pride. Not my ego. But my lifestyle. I rely on my mathematics a lot. To guide myself. This is the way I lead my life. And today I made approximate gamma function. In integral form.

I am finished with KAAL number discussions. And blog posts.

Approximate division by three consecutive numbers

 Here is an approximate division formula. The below divides n by m.

And the Wolfram Alpha screenshot for 1475 by 14.75

Hope you like the expression !!

It ain't over with KAAL number theories

KAAL number theories ain't over yet.

I propose a factor p, defined as below. I propose using p just like mathematicians used i in e, cos, sin formulas.

Here's how, I propose the theory

I have checked the results for x equal to 16, 108, 618 and 1618. The results are satisfactory to me.

Have a nice day, guys !!

With a sample seed of x equal to 227

With a sample seed of x equal to 7

With a sample seed of x equal to 8698

Are these fine ?