Why Qayanat calculus and Approximate integral are correct ?

We have numbers. Fingers.

Then we use ruler or scale.

We measure 7cm.

Our eyes see 1+2+3+4+5+6+7. Though only 7 cm. And We come out with an accurate formula of (n(n+1))/2.

Next step.

We see inches. We don't get confused.  We multiply. By 2.54.

Multiply.

And (n(n+1))/2 is multiplied. We come out with accurate formula of ((2n)!) =2(1)2(1+2+3)2(1+2+3+4+5) . . . .2(1+2+3+4+5+....(2n-1))

We come out with accurate formula in both cases. Possibly proudness. An internal thing.

Qayanat calculus is above psychology. 

Approximate integral the reverse.

Yet another p by q formula

Below is yet another formula for p by q.

Hope you like it.

Have a pleasant weekend !!

Daily Plans

 Mornings

Practicing the bust of head at various angles

Mornings/ Afternoons

PDCA cartoon human improvement.

Evenings

Wacom monochrome practices

Puzzle

 Kirti was a half blind man. He was educated and a post graduate

He remembers his route-path like below.

200 steps straight, then 50 steps left. Then restaurant.

Or. 500 steps right, then 20 steps right, then 300 steps left. Then electronics shop.

Then he had a brainwave and made a model in Braille. 

What could be the model ?

Another expression for p by q

Here is an expression for p by q, the rational number. 

Hope you like it !!

The rational number p by q

 Here is the rational number p/q .

Hope you like it.

An expression on 29th November 2024

I am presenting an expression today.

Hope you like it !!

Getting into Raj Comics

Am I a better artist than Anupam Sinha or his team ?

Certainly not.

Can I get into Raj Comics ?

Yes. It is possible. 

We don't understand.  How?

. . . By marketing.  Marketing Raj Comics.

What?

Why should people buy Raj Comics from you ?

Because I have constants power. Delhi professors can be convinced to buy Raj Comics.

. . . Hmmmmm. You have a point.

Puzzle

Bandhu was the chief of Aroma Inside Ltd.

Sid and Nakul were two managers working under Bandhu.

Bandhu wanted to check how Sid and Nakul maintain their files. Bandhu wanted to reduce old data and keep Aroma Inside Ltd. tidier.

Sid maintains Finance, Purchase, Sales and there in datewise.

Nakul maintains yearwise and there in Finance, Purchase, Sales.

Who is more liked by Bandhu? Sid? or Nakul ?

Puzzle

Shukla was the chief in Hopemann Industries Inc.

Mukherjee and Chatterjee are two men working under Shukla. Both Mukherjee and Chatterjee try to please Shukla by going to any manageable level trying to downsize one another.

Hopemann Industries Inc were supplied raw materials by No Money Needed Ltd. Shukla was irritated by erratic supply by No Money Needed Ltd. in recent times.

Shukla calls both Mukherjee and Chatterjee and asks them to get evidence of erratic supply by No Money Needed Ltd. from the Hopemann's data kept as scanned images of receipts. Shukla said he will be contacting No Money Needed Ltd. in 20 minutes.

Mukherjee and Chatterjee each in order to please Shukla decide to work individually and go through the data.

Mukherjee finds the first instance of erratic supply by No Money Needed Ltd. and goes to Shukla.

Chatterjee waits; decides to get all instances of erratic supply by No Money Needed Ltd. and then goes to Shukla.

Whom is Shukla pleased with? Chatterjee? Or Mukherjee ?

Thanks Internet Community

The bust of head has arrived.

I am hopeful of drawing better heads. And gain confidence in making funny caricatures thereby.

The funny cartoons stay. On paper. In color.

The comics shall be black and white. Over Wacom.

The business idea of delivering customer selfie images stay. In color. 500 rupees for artwork.  And 500 rupees for constant based horoscope. 0, 1, root 2, root 3, phi, pi etc.

Thanks.  Have a nice weekday ahead.

Is it wrong to make (n(n+1))/2 formula continuous?

 Here is the Google AI answer

Decide for yourself!!

My Plans

Comics

Black and white.  Why? Because Roy Lichtenstein does monochrome comics. In paper. Printing charge advantage is there with monochrome. 

Caricatures 

I am waiting for the Human head model to be delivered.  Then practice and see.

SAIL

Steel plants are going green. Meaning minimum pollution.  I shall try and get into green steel.

Good bye for now !!

Puzzle

World leaders meet in Jivanis, Pulsandin.

A 10 cm wide concrete slab is placed at a height of 5 feet in a room

US leader and Chinese leader have to walk from opposite sides and have to exchange big spherical fragile gifts which can be carried if both the hands are used.

Near the centre of the slab are Sri Lankan leader, Pakistani leader, Bangladeshi leader and Nepalese leader watching the show.

Were the leaders from US and China able to exchange the big gifts?

Qayanat Calculus

 

Erdos Numbers

 Erdos numbers of some mathematicians/physicists

Chandrasekhar Subrahmanyam 2

Alladi Krishnaswami 1 (He lived in older times)

Roger Penrose 3

Stephen Hawking 4

Srinivasa Ramanujan 4

Manjul Bhargav 2

Srinivasa Varadhan 2

Akshay Venkatesh 2

Asghar Qadir 3 (From our neighbor Pakistan)

Ritabrata Munshi 3

Sudhir Ghorpade 3

Manindra Agrawal 3

Alon Amit 2

Stephen Wolfram 2

Neena Gupta 5

Renu Laskar 1

Parimala Raman 3

Kalpana Mahalingam 3

CS Seshadri 3

Kamakoti Veezhinathan 4

Srinivasa Ramanujan 3

I am writing from my memory. Do I have a good memory ?

Authorization for comics

 I was having confusion as to what sort of comics should I be making. Manga, Superhuman, Tintin, Archies, Amar Chitra Katha, Diamond, Raj etc.

I had to follow one of them. And draw at their level. Only then can I be expected to be absorbed by them. 

Then I came across this comic drawing book. By an American Roy Lichtenstein. The drawings are a little simple. Moreover, it is monochrome. And it offered me the opportunity to say I have a guru.

I have ordered the book.

So practicing head drawing from the head I ordered and drawing comics from the above book will I be doing in present and future.

Have a nice day, folks !!

New focus in artistic endeavor

I am tempted a lot by drawing art. I have a lot of greed in drawing my art very very good. I started off my artistic journey by following what R K Laxman did. Cartoon jokes and caricatures. 

I thought because I have formulas in golden ratio; I can become a very good artist. But not quite!!

I thought my caricatures of VIPs were decent. But golden ratio did not help to improve further much.

So I made a plan. I decided to get myself "Statue Drawing Ability" on my own.

So I bought this item from Amazon India.  I will draw light and shadows of it and thereby improve my portraits/caricatures drawing ability. 

Namaste 🙏 

India's new spin proposed

I am proposing new spin for Indians. India is the most populous country in the world. 

Instead of 1,2,3,4 . . . ; we must develop 1, 1+2, 1+2+3, 1+2+3+4, . . .

Instead of saying we have 4 family members. Namely 1+1+1+1; we will be saying 1+2+3+4 = 10 family outputs. 

Look at the below expressions. 

These formulas and the work in development of the formulas will benefit civil servants, military and social activists.

I request influential guys to consider favorably,  development of the mathematical system for this thought.  I may be included in the team too.

We have blessings of my Jesus.

Unique result

Consider

And

Add the sum of expression above. It can be delivered by a single result given below. And all the three have similar base of ((-1)^n)((4^n)/((2n)!)

Have a nice weekend!!

Cos(x) and Sin(x) expressions

 

Also

Sin(x) takes more parameters

You may be aware that I have approximate expressions for factorial,  to the power n and the next number. 

So I tried on Wolfram Alpha using above.

I always thought where there is cos(x) , there is sin(x). And they have same number of parameters.

But not so.

The above happens at only one place. At x = 4 or x=1/4 depending on whether x^n is in numerator or denominator.

Have a nice day!! May God bless us !!

Approximate Integral?

 

Now that we in India have approximate 2n  factorial formula; and now that we in India have approximate (a/b)^n formula; and now that we have the next number approximation; and now that we have many other formulas for approximate functions: . . . . . . it is time that Indian mathematicians apply their brain and work towards approximate integral. 

Just as Taylor series gives function as infinite series of to the power n, factorial and next level derivative; I am suggesting a function of approximations with my approximate values of (a/b)^n, (2n)! and next number. 

PM Narendra Modi should form a high power mathematics committee to explore, try and make approximate integral statements. 

The benefits are Indian people will develop to behave approximately. Indian people will improve intelligence.  Indian people will develop devotion.

If you think my idea is even 10 percent feasible, do comment below. 

Is our Bhakti due to gravity?

Imagine you never experienced gravity. You were born in space, devoid of much gravitational field. Will you be having bhakti for Shiva? For Vishnu?

Sitting in my home at Ranchi, I am hearing devotional hymns and chants being played on loudspeakers.  Chatt festival season, it is. A local festival of Bihar and Jharkhand. 

Can there be taal without gravity? Imagine tabla being floating around. Can a tabla player still play the tabla? If he cannot, then there is no rhythm.  If there is no rhythm,  then there is no hymns. If there are no hymns, how can bhakti be developed?

My earlier approximate formula for 2n!, I believe is devoid of gravitational numbers.  So I claim. So I believe. 

My point is this.  Rhythm may not possible in absence of gravity.  Is it possible to see truth, meaning God through my 2n factorial formula?

I wonder.

2n factorial - Final submission

 The (2n)! formula with ((((n+1)(n+2))/2)^n) gave me many sleepless nights since April 2024. On April 2024, I discovered that ((((n+1)(n+2))/2)^n) is approximately connected to (2n)!. But how to give an expression? My education is limited. My mathematical prowess is hardly comparable to champions of IIT JEE.

But I felt it is my duty to complete the formula. Till calculator range. Till 170!. Or when n equals 85.

I carried on. I used the formula of Stirling formula and other expressions of (2n)! to get (2n)! through ((((n+1)(n+2))/2)^n). Well that was incorrect method. But I continued.

Now, I have finally made it. Without the use of any other approximate or accurate formula of (2n)!

Here is the formula

Here is an excel sheet that confirms 99 percent accuracy.

Have a great weekend folks!!