Semi realistic to realistic to hyper-realistic portraits

Currently I am a semi realistic portrait artist in color. 

I want to get into hyper-realistic color portraits drawing.  I don't know whether it would be feasible or not. Whether I have the theory.  Then possibly 60 hours of work.  Then rendering.  Control in shading.  Eraser don't work in color. Then limitations in artistic ability. I have only skin colored pencils.  Not a 132 colored pencil set. Then my pencils have to be sharp. Currently I am comfortable working with blunt pencils. 

But I have 3 days of holidays in the next 4 days. I shall be thinking and trying on whether I can manage hyper-realistic drawing or not. Thankfully there are high resolution images over internet. So source of image is not a problem. 

If my project is successful then I shall go ahead with a higher resolution camera and 132 colored pencils set.

I shall fully apply my mind, my brains and my hands these three days and let you know whether I shall try for hyper-realistic colored portraits or not on Thursday.  6th October 2022.

Happy day to you!!

Traditional Indian mathematics taught and my claims

This blog post is about the traditional mathematics in Indian syllabus in schools.  And my claims supporting inclusion of consecutive numbers in the syllabus. 

Functions,  algebra, trigonometry,  Maclaurin series,  Force of Newton and calculus are the main categories in the education today. Most of the topics develop children to think.  Most of the topics encourage the children to discover the external world. 

I put forward my claims of consecutive numbers. They will help children to understand infinite series,  mathematical constants and binomial operations.  These concepts will help children in their IQ. These concepts will help children to discover internal world.

Today the education is restricted to mostly scientists and engineers.  Arts, commerce, diploma students don't have exciting topics.

If consecutive numbers are included in syllabus arts, commerce, diploma students will have interesting topic.

When we write 1,2,3,4,5 . . . 10; most of the kids will think numbers are increasing by 1. Little do they realize that there is decrease in numbers too; if looked the other way.

Consecutive numbers form has plus and minus both symbols.  The above mentioned confusion do not arise. 

These are some points. 

My portraits story

I took up to drawing faces because I was not with my family here in Ranchi. I am staying with my mother.  I have sufficient time and do portraits,  cartoons and caricatures. 

I do portraits because one gets to spend one hour of time. I do cartoons because I feel my sense of humor is high. I do caricatures because I feel I am good in drawing resemblance of a face.

I approach portraits in two ways. Both of them colored and not monochrome.  The first approach is only using Mont Marte skin colored pencils. 

The second approach is using Camlin poster colors and then when the painting is dried then using Mont Marte skin colored pencils. 

Both of them have been traced using Brolaviya mobile stand  and DaVinci eye app in HB pencil.  Though my resemblance in portraits is good (from the feedback got from readers) I reserve resemblance for caricatures.  I trace also because most of the subjects are VIPs and basic errors should be avoided at least in portraits. 

I would like to propose a theory here. What happens when an image is enhanced by changing colors by using digital image tools. I think the affected areas exhibit the property of water and not light. This statement of mine requires citation from scientists and experts.  However my point is; suppose the image is enhanced and suppose the affected area exhibit property of water. Then what? Then to me it means using watercolor.  Because there is water in watercolor. 

Well, that is one part.

Another point I wish to make is doing realistic Portraits nowadays requires no great skills. Only precision, being systematic and perseverance for long hours.  Great realistic Portraits take upto 7 hours of time. I cannot manage beyond 1 hour.

The reason I don't spend more than 1 hour is probably due to four reasons. 

1. Not sure of planes of face from the image because of two or more lights when the photo was clicked.

2. Not focused on perfection due to lack of focus and lack of training. 

3. Unable to render better 

3. Lack of patience 

There are three solutions to attain perfection in colored portraits. 

1. Using your own camera.

2. Finding a guru or sitting with young realistic artists and doing a project together. 

3. Using a 24 skin colored pencils set instead of the now 12 pencils set.

Do you feel differently? Would you like to say something?

Please let me know. 

Approximately finding (x/a) to the power n

Suppose you want to find the square or cube or to the power 4 etc. of a rational number (x/a).; can it be done using binomial? Approximately yes.

How about that ?

Here is the approximate formula. This formula has many practical applications like agricultural growth calculations, population calculations, space calculations etc. etc.  Binomials are natural. More so are the binomials of consecutive numbers. And simply dividing the binomials raised to different exponents gives the to the power of the rational number formed by the two terms of the binomial.

And here are the screenshots of Wolfram Alpha which validates the formula stated.

Hope you have a nice day !!

Need of the hour

The need of the hour is to give thrust to consecutive number.

Many. many thanks to Wolfram Alpha. You have been great. You have helped me in expressing myself.

I have made this post to show again in one place how consecutive numbers give expressions for important constants.

Constant e

Constant pi\

Constant Gamma

Constant Golden Ratio

Apery Constant

Catalan constant

Gauss constant

Consecutive number model or Rational number series are great in constants, binomials etc. Also infinite series can be easily taught as expressions cancel one another.

I wish all the best.  Have a nice day !!

New expression today

New expression is posted today. This expression is similar to the expression posted yesterday. In the sense that it is a binomial expression stated in a certain fashion. Like the expression posted yesterday, this expression too is approximately correct. However, it is as interesting as the expression posted yesterday.

Here is the expression.

In the above expression modulus n2 is less than modulus n1.

Here are the Wolfram Alpha screenshots to confirm that what I have stated is true.

Have a nice day !!

New expression

New expression is being posted today. This one is very interesting. You add up two binomial statements expressions in some way and what you get is very surprising indeed. Zero !! It is not actually zero but approximately zero. 

How about that ?

Here is the expression

The above equation is valid whether n1 is negative or n2 is negative. The only thing is modulus n2 is lesser than modulus n1. I have checked.

Here are the Wolfram Alpha screenshots with an example to show that the statement is valid.

Have a very nice day !!

Two more prime number generators

Two more prime number generators are hereby presented.

Consider the following statements.

Have a nice day !!

Expressions on 13th September 2022

The following sets of expressions are submitted today, 13th September 2022. Also submitted are Wolfram calculations to confirm that the expressions are correct

The first set

The second set

Hope you like them.

Have a very nice day !!

. . . . and 4 consecutive numbers

The 4 consecutive number model satisfies only one expression. Not three as in 3 consecutive number expressions posted in my earlier blog.

And that is

And below are the Wolfram Alpha tested screenshots to verify that the expression is correct.

I would like to stress the following points for Modi government to consider for inclusion of consecutive numbers in curricula.

1. Mathematics should not be restricted to scientists and engineers only. Commerce, arts, diploma, fine arts, music students should also know mathematics. And consecutive numbers are interesting, important and effective mathematical knowledge piece.

2. Consecutive numbers theory are nature driven. Examples from nature can be given.

3. Reciprocal of consecutive numbers say a lot on number systems.(I have already written about it)

4. Finite addition of consecutive numbers result in consecutive numbers

5. Finite product of consecutive numbers result in gamma function.

6. Consecutive numbers theory are closely associated with golden ratio

7. Infinite series can be taught to commerce, arts, diploma, fine arts, music students .

8. Important mathematical constants like pi, phi, e, gamma, Apery constant, Catalan constant, Gauss constant can be learnt from consecutive number model.

9. Binomials can be learnt from consecutive number method.

10. Last but not the least, students having consecutive number knowledge will feel like lions and not shy domestic cats. The personality and ability of the students will improve and the students will roar and bring India to top position.

I beg to Modi government to include consecutive numbers or Rational number series into our curricula. My papers are with JETIR which is Gujarat based. 

Further to earlier post

In my earlier post we saw how 3 consecutive numbers taken as numbers and factorial gave us important results. 

The earlier post had infinite series. 

In this post I show how 3 consecutive numbers taken as numbers and factorial give important results.  In binomial. 

I have checked the correctness of the expressions in Wolfram Alpha. I am attaching the Wolfram Alpha screenshots too.

Have a nice day!!

My intuition on hands and fingers

When I began my mathematical journey, I had nothing but intuitions and number mantras and an intuition in infinite series. It was Wolfram Alpha which I used, very generously, to get results. 

Thank you Wolfram Alpha

I am presenting the following write-up today.

Have a nice day !!

State of my mind

Internet over mobile is what this blog post about. And what is going on in my mind of the internet world.

Chess

I play chess games and my Elo rating is greater than 1600. Class B player. I have played with online players too and have won 4 and lost 5 games till now with 1600 players.  I use ratio principles in analysis and moves because golden ratio is my strength. My favorite site is lichess and I like their Stockfish very much.

Art

I daily try to tell a joke through my cartoons.  If you are not aware of this then here is the link. Sometimes I draw portraits.  Sometimes caricature.  I find art as very tempting.  I want to master all the areas of art then I realize that I am 54 years old. I watch YouTube videos in art and pick up ideas.

Mathematics 

My stock is over. I have written about it all. Perhaps I should focus on Indian Olympiad of Mathematics; but I don't.  Because I find this idea immoral and greedy. Maybe I will read Theory of Complex functions book that I have.  But it is tough.  I browse Wikipedia for mathematical related matters. 

Slow jogging 

I plan to slowly jog a distance of 1 kilometer daily. I feel slow jogging more suitable than walking. 

That's all folks.

Have a nice day. 

Summing up on binomials

Newton made the basic binomial statement. There is nothing more basic than that. And nothing more simpler.

Cauchy too made a binomial statement. It was sigma and product equivalence. I thought it was brilliant. But somehow not so popular here in India.

Abel was a cute young gentleman who died in poverty. (Blessed are the poor for they are children of God). He made very beautiful and tough binomial statements. I have managed to collect two of his statements and made a blog post earlier.

The above are of binomial distributions.

Then Gauss made normal distributions.

Laplace made Laplace distributions.

In this blog post, I have summed up my binomial statements and listed them into four major statements. My binomial statements are inspired from consecutive numbers or the Rational Number series. I wish to state here that Rational Number Series are not only suitable to binomials but also in infinite series and in golden ratio expressions. I wish to state that Rational Number series are of nature. The front paws of a dog are different than its rear paws. That sort of thing is what Rational Number series is all about. But my claims fall on deaf ears. 

Anyways.

Here is the summing up sheet of binomials.

I wish I could read more. I wish I could get library cards so that I can lend for myself great mathematical books. I wish I had 20 lakhs of rupees to spare for books.

Anyways.

Have a nice day !!