Zeta(2) or Basel Problem or pi squared by 6

This problem was called Basel Problem. Bernoulli posed this problem. Leonhard Euler, a young man in his twenties proved it. It was a phenomenon in mathematical circles. Euler earned fame. He was called by the King of Prussia himself. He made mathematical theories due to which he is called 'King of Mathematics'. He has left so many theories that not all of them have been comprehended. He slowly began to loose his eyesight. But not his mathematical insights. Leonhard Euler was so great.

So Zeta(2) or Basel Problem or pi squared by 6 is given below as computed by consecutive numbers.

Have a nice day !!

Zeta(3)

Zeta(3) which is Apery constant is calculated by consecutive numbers. I thought 1/n^2 and n/(n+1)^3 will be calculated separately but not.

The following is zeta(3).

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Zeta(7)

 The zeta(7) expression with consecutive numbers is given below

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Zeta(5)

Zeta(5) is now well expressed with consecutive numbers.

Below is the expression

And Wolfram Alpha screen to confirm the above.

Nice weekend guys !!

Art Issues

Apery Constant and Consecutive Numbers

Roger Apery stunned the whole world when he considered the Riemann-Zeta function for 3. He moreover proved the irrationality and stated transcendental properties for zeta(3).

The Riemann zeta function for 3 is now called Apery constant, honoring him. The value of Apery Constant is 1.2020569 . . . . 

Now, with the help of Wolfram Alpha, I combined the concept of Apery constant and consecutive numbers. And have made the following statement.

I hope you like the above expression.

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Objectives in drawing art

 

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Google AI says practice exteriors and interiors

 

Google AI says my hands drawing are good

 

A Steep Target and Financial Losses Ahead

The challenges I face are similar to what Gujaratis face in running the government. In comic drawing.

Steep Targets and Financial Losses Ahead.

In comic drawing, I need to get into exteriors. It is a steep target. I have to begin from almost a scratch. And then interiors. This is also a very steep target. In interiors, I need not start from scratch, but still very difficult.

Above all, match interiors and exteriors with humans and animals. In proportions and perspective. 

Then, why did I start ? Because I wanted to tell stories.

Why do I think Financial Losses ahead ? Because my comics 'Behavo' is a failure.

But I have decided and plan to be focused. And continue. In digital, it will be complete comic drawing. And in paper, colored pencil drawing of Hindu Gods.

My golden ratio abilities, my bhakti shall be my guiding force.

Jai Mata Di !!

To do PDCA

 To Plan and Do in one drawing.

To Check and Act in another similar drawing but with different camera angle

I plan to do these in Microsoft Paint. The improvement. I plan to do shadings. I intend to practice PDCA for three months. 

I have stopped other art like portraits, caricatures, funny cartoons etc. for now. I plan to do above and Perumal hyper-realistic drawings. I wish to concentrate on these two only.

Have a nice day !!

Further to earlier post

In the earlier post, I explained the drawing steps that I plan to take.

This blog post is further to the previous blog post. In this blog post, I explain the Fresnel rings drawing. 

With this I have completed the "man doing an artwork" phenomenon in mindset and in spirit. Only thing left out is possibly mind-eye-hand co-ordination and its ability.

Wish me good luck. And best wishes for hard work towards my objectives.

Drawing Steps

 

Paper Drawings ?

The digital drawing objectives are clear to me. Comics and cartoons.

But I feel guilty that I am unable to do paper drawings. Not that I am good. But due to greed at that point of time, I bought Faber-Castell 120 pencils set. About 15000 rupees and unable to justify much. 

Also I have two sets of Mont Marte skin colored pencils. Two sets of Crayola skin colored pencils. Two sets of Crayola skin colored wax crayons.

Only justification is my funny caricatures are okay-ish. 

The digital world is big. Cannot beat the digital world of art.

Thanks for hopping in. Have a great day !!

Towards dream objectives

Drawing

• Practices

1. I plan to copy drawings from Jyotsna Prakashan books that are with me. Pratap Mullick, Rahul Deshpande , Nandurkar and others. This will improve my drawing abilities
2.  PDCA practices for comic drawing.

• Theory

        I have many books by great authors like Giovanni Civardi, Andrew Loomis and others.

Mathematics

• I plan to allocate budget and  make a list of a few books on Abel, Gauss, Euler and others. I shall later before retirement buy them.

Music

• To listen to and appreciate Anirudh Ravichandar, more closely.
• To listen to and appreciate Sachin-Jigar more closely.

Physical Activities

• I like cleaning cars and polishing them. I have all the necessary materials for polishing cars. Car is a great invention and I feel like cleaning and polishing regularly.
• I enjoy shopping for things and easily am able to allocate time to make shopping lists. I usually buy things after leaving office and before entering my quarter inside our SAIL colony. Tribal paintings are one of the more exquisite purchases that I have made.

A comic frame to the best of my ability

 

Complete Drawing

 I have added highlights too. Now this art is complete.

Changes made to my drawings

Also, unnecessary borders to be avoided. 

(Tomorrow,  I shall try light highlights too.  That will be a complete drawing. Wait for tomorrow)

Prepared for both digital and print

I am prepared to draw comics on both digital and print media with Clip Studio Paint.

It will be colored on digital media.

It will be grey scale on print media, to reduce costs.

However the journey of quality improvement is a long long journey. Humans are okay. But animals, objects, buildings, vegetation etc. need a lot of improvement in days to come.

I am working towards that. I want my drawing ability to be like writing ability. Simple, sufficient and suitable. 

Have a nice day !! 

Direction of Mathematical spirit of mine

 The last 3-4 months were very difficult for me. In my mathematical frame of mind. I had done constants, approximations, binomials and little combinatorics. But the Indian mathematics ether in India kept me disturbing.

It all started when I worked on approximate (2n)! formula. This formula could calculate approximately decimal factorials too. Because it could calculate decimal factorials approximately, I made a blog post of Approximate integrals. And because I talked of integrals, I extended my thoughts to 'Qayanat' calculus. And then I went into Newton calculus and Leibnitz calculus.

I am up to 95% clear in Newton calculus. But not so with Leibnitz calculus. 

Then my thoughts moved to Euler and the complex number i. And the work of Euler in Taylor/Maclaurin series.

I am awed by the work of all the above mathematicians and told myself that they were all so superb.

Now these two below are giving me peace. Differential of e to the power mx. Integral of e to the power mx. And I have equated them to sigma till infinity expressions.

Putting m as i will give you Euler thoughts.

Putting m as a(a+1)/2 gives my thoughts.

Then what happened to my 'Qayanat' calculus? Well, I do not think 'Qayanat' works as functions. 'Qayanat' is a reality. If mathematicians are interested to understand 'Qayanat' my way, then they can call me for a talk.

And if you want the world to be represented as functions, then there is nothing better than Newton calculus.

Happy new year to my blog readers !!