The Euler- Mascheroni constant, gamma made easier to represent with consecutive numbers model. I feel delighted that the Lord above helped me in representing a great concept of gamma very simply.
The expression
You may observe that there is only one 3 consecutive number function in above.
Just one or two days and then there is Weekend. May good things happen and hope you are happy. Have a nice time.
The expression is complicated. I thought let me share the text I typed.
Yesterday I was working on some expressions where in gamma came across. I wanted to isolate and make a new expression of gamma. But I could not.
Today morning I thought let me try with a standard formula for gamma, but with consecutive numbers. I made such an expression. My earlier gamma expressions involve integrals. But this one does not. It involves 3 sigma expressions, one log function and three consecutive numbers function at two places.
Here is the expression.
Have a nice day !!
You may be aware that I am deeply interested in two things. Mathematics and drawing art.
As not much help is coming from the Indian society at large, I have decided to take things on my own and develop my thinking in mathematics and drawing art. Indian societies are possibly of education. And not of scholarships.
Mathematics
I have decided not to go after German, American or other mindsets in mathematics. But develop English sense of mathematics. With journals difficult to get hands on, I have decided to concentrate on the following English books on mathematics.
1. Algebra by Hall and Knight
2. Trigonometry by Loney
3. Calculus by Abbott
4. Pure Mathematics by GHHardy
5. Carr book (Ramanujan followed this book)
Drawing Art
Most of the artists over Internet think of "A Box" as the basic drawing element (Stage 1). But quite frankly, I am unable to internalize it.
I find it easier and in resonance with "A Triangle" as the basis for drawing my artwork.
Yesterday, I thought on the box and triangle issue. And decided on solid triangle. I told myself either perform or perish.
I wanted to apprise my blog readers on the above plans which are totally the final ones.
Summing up on my two sets of Golden Ratio
There is an advantage with my model of consecutive numbers. Terms may cancel out one by one as we tend to go to infinity. And what we are left with is the first term. This rule was used in the above. And I got Golden ratios expressions between Good Friday and Easter. Perhaps, it is the faith of St.Thomas, the apostle of Jesus Christ.
Have a nice day !!
I combined all the strength of consecutive numbers, focused with all my abilities and got for myself 1 by golden ratio. Also the golden ratio.
These are new expressions. I had never done these earlier.
Happy Easter Sunday, in advance.
My Perspective workbook for comic art has been delivered.
It is superb. One is guided into drawing. There are Perspective grid pages and the reader is expected to draw along with the author.
Thanks, dear author and dear publishers.
Have a nice weekend, folks !!
On October 29, 2024, I made the following blog post.
Today I am typing the above out in symbol form. The symbols are so great invention. Foreigners are awesome and geniuses.
Have a nice day !!
We all have learnt the expression for 2 to the power k, in our school days.
Here is 2 to the power k in 4 consecutive number form in an infinite series.
I have below combined the above two results and have typed it out in Microsoft Word.
Hope you all like the expression. Have a nice day ahead !!
I am using Sivi app to improve my spoken English. I am decent in spoken English. Possibly Sunil Gavaskar level. And not Harsha Bhogle level. I hope you have understood me.
I make grammar mistakes ; in or on types and mixing tenses. Arya my AI trainer helps me in correcting my spoken English.
Have a nice day !!
Are you a mathematician ?
I am an electrical engineer graduated from Kumaraguru college, which is managed by N Mahalingam group. I have an inspiration for mathematics. That's it.
People say you hate Gauss ?
Absolutely untrue. Gauss is a legend. Vested interests spread these rumours to get milage from narrowing VISA system.
What is your secret behind mathematical sense ?
Timing. Every 24 hours has a day. Has a night. This timing thing should percolate in mathematicians like no other. Only then they can do advanced mathematics.
You seem to have an easy time with mathematics. Do you agree or not?
I don't agree. I had very difficult time in making understandable expressions. I had to literally milk a bull for milk. Fortunately Wolfram Alpha is there and now I have some expressions.
You said you are an expert in convergence. What do you say about this ?
Please don't put words in my mouth. I said I have a thumb rule sorts for testing convergence. Not an authentic convergence test.
You said 1,2,3,4,5,9,10. Why?
Please don't ask such questions. There are already many controversies around. I suggest you be responsible.
Very well, do you have concepts of convergent value?
No, I don't.
Thank you
Thank you
It was difficult to maintain my books and art materials. So, I bought a steel almirah. This steel almirah has only horizontal racks in them.
I have kept my books and art materials inside it.
Whenever, I feel like doing a paper art, I take out the necessary art materials and do paper drawings. I later keep the materials back. This steel almirah storage and retrieval and keeping back works for me. I am disciplined.
Happiness and joyful is what I pray. And I pray for all.
Expressions of the type (j*j-2+1/j)/2 and (j*j-2-1/j)/2 can be decent prime number generators. They have an efficacy of 49%..
Bye, bye !!
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(5) is now well expressed with consecutive numbers.
Below is the expression
And Wolfram Alpha screen to confirm the above.
Nice weekend guys !!
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.
Have a nice day !!
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 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 !!
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.
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 !!
Drawing
Also, unnecessary borders to be avoided.
(Tomorrow, I shall try light highlights too. That will be a complete drawing. Wait for tomorrow)
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 !!
