And Gamma function

Here is a gamma function.

And the Wolfram Alpha screenshot for 3.75!

Have a nice day !!

Let us recapitulate KAAL number

A lot has been written about KAAL number. There are possibly many confusions because I tried "too much" to make them "accurate". Also I was "hell-bent" on making a gamma function.

This blog post straightens many things.

KAAL number is (Kirtivasan, Abhaya, Akshaya, Lata) number.

Its value is 4.4

I am not doing any gamma equations with KAAL number.

It gives approximate results. Not any of the results are accurate. That is the beauty of KAAL number. Its beauty lies in its approximations.

Write up

I am using a number 67.89 in all the below expressions.

Infinite series RHS

Infinite series LHS

One(x)

Zero(x)

Expression 1

Expression 2

I wanted to finalize my expressions on KAAL number. I am not getting into gamma functions. I am not making 4.4 more accurate.

Goodbye for now !!

Combination now made continuous

The combination formula binomial(n,r) is now made continuous. This means that one need not go back and forth or up and down but keep moving ahead.

Here is the formula and an example with it.

That is why binomial distribution are so natural. It is continuous. 

I feel ecstatic. I hope you like the expression.

Below is the Wolfram Alpha screenshots for binomial(7,2) and binomial(8,3)

Have a nice day !!

Childhood Dreams

Right from my childhood I would wonder why there is no formula for a^n-b^n and a^n+b^n.

I have fulfilled this dream of mine yesterday. It took me whole Sunday to do that. 😄. My mathematical prowess is weak. But my intuitions are okay, I guess.

Here are the formulas.

They are not exactly a^n-b^n and a^n+b^n. But the values can be computed.

Have a nice day, guys !!

Zero

Here are results of zero obtained from binomial.

And my master, King Christ

Binomial results

 Here are two more binomial results

And the Wolfram Alpha results to confirm they are correct

My three consecutive number model fetch all the major constants.

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

From the last two blog posts

 This result is the combination of the results posted in my last two blog posts.

This result is interesting because children often wonder there is a formula for (a+b)^n but no formula is there for a^n-b^n. Now these children have something to feel happy about.

The formula is

And the Wolfram Alpha screenshot to confirm above is true.

Have a nice day !!

This result too

 The following expression is similar to the expression in my earlier blog post.

And the Wolfram Alpha screenshots to confirm the above is correct.

Have a nice day !!

Result from Intuition

 Most of my mathematics was developed from intuition. I would have an intuition. And I would type them in Wolfram Alpha. And the results were obtained. 

Many, many thanks to Wolfram Alpha for I was able to express my intuitions mathematically.

The following result is also one from my intuition. 

Here are the Wolfram Alpha expressions to confirm that the above expression is correct. I have used a equal to 5, b equal to 7, m equal to 4 and k equal to 6.

Did you like the expression ? There are two standard binomial statements on RHS multiplied by two algebraic expressions. The numerator binomial statement starts from 1. The denominator binomial statement start from 0.

Have a nice day, guys !!

Related to KAAL number?

KAAL number is a memory of a few months.  

Yesterday,  I did an expression and got 1 by e. Today,  I tried the same expression with alternate negation.  I got 0.216. And inverse of 0.216 is about the same value as KAAL number. 

This is interesting. 

1 by e

 I was thinking about something, when the expression on the LHS, came into my mind. I wanted to find out whether the expression on LHS results in something good.

Yes, the expression results in 1 by e.

And below is the Wolfram Alpha screenshot to confirm that the expression is indeed 1 by e.

Have a nice day. Have a nice weekend !!

Three ways to look at my drawing objectives

There are three ways to look at my drawing objectives which are to be achieved in 2 years time.

First way - To draw like masters

Second way - To achieve perfection in pencil control

Third way - To reach art level 80 in the eyes of AI.

Of course,  I shall be working on still life drawings,  outdoor drawings,  comic drawing and cartoons and portraits.  But above are the improvement plans.

I hope you have understood my expectations from myself. 

Weekend is nearing. Have a great weekend,  guys !!

My truth

This is my present best shaded hand.

Art Improvement needed (in one year)

1. Exercises for form Bending 

2. Exercises for form carving

3. Exercises for form agglomeration 

4. Exercises for form mannequining common creatures, humans, objects

5. David Finch shading.  Giovanni Civardi shading.  Both

Mathematics Improvement needed (life long)

1. Hypergeometry self learning 

2. Digamma self learning 

3. Bessel functions self learning 

4. Whether complex functions too ? ( wondering!!)

Music Improvement needed (short term - 2 months)

1. Finger movements and playing in harmonium 

Personality Improvement needed (as much possible,  daily)

1. Regularity in 15 minute Vipassana 

2. Regularity in prayers,  sandhyavandanam 

Have a nice day,  guys !!

Till the foldable chair arrives

My foldable chair will take time to arrive. Then I shall begin Ranchi township sketching. 

I am presently using my sketch book, pencils for indoor drawing. 

Here is one I did.

I shall follow the same style for outdoor sketching too.

To have clarity

To boldly use pencils.

There is a door. There is a refrigerator.  There is a curtain. There is a clock. There are two switch boards. It is a section of my main hall in my quarters. 

I hope you like the drawing. Have a nice day !!

Three desires in drawings

Frank Rines in landscape 

Proko in anatomy shading 

Kim Jung Gi in comic drawing 

My Drawing Art Plans

In this blog post, I am outlining my drawing art plans.

1. Drawing Exercises 

Mirroring 

Drawing alphabets extrusions on planar surfaces 

Drawing alphabets extrusions on spherical surfaces

Extrusions and Intrusions. Addition and subtraction of drawing alphabets. 

Carvings 

2. Actual Drawing Practices 

Still life drawings inside 

Ranchi township drawings 

Human Anatomy shading 

Comic drawings 

3. Time Frame of 2 years

Above is the drawing notebook for Ranchi township drawings. 

And below are the foldable chair for outdoor drawings and human anatomy book ordered by me from Amazon. 

My hobby pursuits planned

My blog posts are mainly autobiographies. I write about my plans, action plan and steps taken towards action plan.

This blog post is no different. 

Drawing Exercises 

I plan to concentrate on spherical and circular paths for drawing exercises.  This is because I am strong in constant pi. I also expect to be driven by constant phi and hope to get higher perspective proportions correct.

Music

As I am concentrating on compositions only, I plan to do 4 finger movement exercises only.  In my harmonium. 

1. Sa, Ri, Ga........ And backwards. 

2. Sa Sa, Ri Ri, Ga Ga........ And backwards.

3. Sa Ri Ga, Ri Ga ma, ....... And backwards. 

 4. Sa Ri Ga ma, Ri Ga ma pa, ..... And backwards. 

These exercises are sufficient to improve my finger movements and develop enough competence to play for compositions. 

(Ilaiyaraja is playing today and tomorrow in a concert at Chennai.  I badly wanted to attend. But money saving is important to me at present due to personal commitments.  Not able to spare money for show. Shall watch in Sun TV from 3pm if possible).

Mathematics 

I am trying to give R&D angle to my mathematics,  currently.  I don't want to write more, now. I work in RDCIS,  Ranchi. 

That's all for now !! Have a great weekend  !!

Vipassana

 

I was confused as to how I should lead my life. With respect to religion.  With respect to religious practices downloaded from ancestors.  And with respect to my drive. And with respect to world peace.

I want to follow ten commandments. 

I want to do Sandhyavandanam.  It is not entirely wrong as per ten commandments to do Sandhyavandanam.  As you are following your gurus and Rishis. And Gayatri mantras are vibrations of nature only.

I want to do meditation.  I found yogic way of doing meditation confusing and difficult.  Then quite recently I came to know of Vipassana.  The Buddhist way of meditation.  I find Vipassana very suitable to me. Vipassana is not against ten commandments as it is of finding peace of mind for yourself and in yourself. 

I shall be visiting temples too. Most of the temples have Shiva Linga.  And worshipping Shiva Linga is not fully against ten commandments. This is my personal thoughts. 

I shall read, study and master Matthew,  Proverbs and Psalms from Holy Bible. 

So that's me.

Ten commandments.  Sandhyavandanam.  Vipassana.  Shiva Linga.  Matthew.  Proverbs.  Psalms.

For world peace.  For better understanding of working of nature and humans and myself. 

Behavo comic has 1K readers

 

My Behavo comics over Tapas has now reached 1K viewership. I feel very happy to announce this.

This weekend is coming to an end. Have fruitful weekdays ahead. Good wishes!!

The 5 variable binomial

 I call the variables man(m), woman(w), kid(k), God(z) and Love(l)

Have a nice day !!

cos(x) and sin(x) now expressed in consecutive number format

For those who have been reading my blog would know that I managed to express pi, phi, 1,0, root 2, root3, Euler-Mascheroni constant, Apery constant, Gauss constant, Khinchin constant in terms of consecutive numbers model.

Now I have managed to express the cos(x) and sin(x) too in terms of consecutive numbers model.

Here it goes

The first two are the Maclaurin series for cos(x) and sin(x); and the next two are consecutive number series of cos(x) and sin(x).

The consecutive number model is so rich. One is sitting in a bench. One person passes by. Then a second person. Why? A person is waiting in office for lunch. One packet is distributed. Then the second one. Why? A person is choosing potatoes in a vegetable shop. He selects one potato. Then the second one. Why ? 

There are so many Whys with consecutive number. One can become a sanyasi too using consecutive number method for meditation and analysis. 😄😄Consecutive numbers are that powerful.

This is nice

This is nice.

What do we get if we add numbers and divide by their multiplication and add the resultant all the way  till infinity ?

We get 3 times e by 2.

And the Wolfram Alpha screenshot to confirm that this is true.

Have a nice weekend guys !!