I am presenting hereby an approximate expression.
Have a nice day !!
Root2 and it's beauty was discovered by Greeks. Root2 is one of the major truths of our mind, our nature, our nature's symmetry and of our God.
Here are 4 root2 expressions I have managed over the years.
Have a nice day !!
I thought let me outline my plans of 22 drawings per day. My plans are like this.
A. ) A human walking , say
1 drawing of normal cartoon variety
3 drawings above head camera or at ground camera or normal
3 drawings above head camera or at ground camera or normal and different than above 3
7 drawings
B. ) A human sitting , say
1 drawing of normal cartoon variety
3 drawings above head camera or at ground camera or normal
3 drawings above head camera or at ground camera or normal and different than above 3
7 drawings
C. ) 4 drawings of one animal, say cat
D. ) 4 drawings of another animal, say dog.
So total 22 drawings.
I don't want to include objects as most of the objects are table, chair, sofa, bed etc. Which are easy and need to be drawn in context only.
I have Frank Rines Landscapes book. And I shall practice by copying.
I have done today's quota. In the morning. I use both pencils and black ballpoint pens. I do drawings in normal A4 sheets. I have bought a JK paper A4 bundle for this. About 6 A4 sheets shall be used per day. I use both sides.
Have a nice day !!
My practices in comics drawing is going on. I am focusing on humans, animals and objects.
Interiors and exteriors are also practiced but not that much. And frame composition, inking and story telling are needed. But not now.
I want to achieve the level of Alex Raymond who made Rip Kirby comics. I am fascinated by his illustrations and want to be like him.
Thanks for hopping in. Have a nice Sunday !!
I present the following expression today
I have typed the expression again in Word
I hope you like it !!
Comics are a great medium. Probably greater than movies. Because of images. You can show how a root of a plant grows below the ground. The same thing is not possible in a movie.
Now I have made a roadmap for my comic art journey. I shall be self learning. I did not join a course because of foreign exchange.
The roadmap.
One drawing takes maximum 2 minutes. I shall be using the time available to me at home here in Ranchi. I am staying with my mother. And have 4 hours of free time. I shall be drawing with my Bose system playing the music in the background. 😆
There are three reasons why I believe there will be improvement in drawing abilities.
1. The 5 perspective poses namely 2 into 50% and 2 into 75% and 1 into 100% worked for me in becoming a cartoonist.
2. I have a theory that 3 sided triangle need to be accurate while 4 sided irregular polygon need not be.
3. I have been working on golden ratio. Phi formulas.
Occasionally, To the point cartoons and sometimes portraits will be drawn and made into a blog post in My Cartoons blog. For your entertainment.
Today is a holiday for me. SAIL foundation day.
Here's wishing that you have a pleasant day. Good bye!!
Today, on 19th Jan 2024, I am presenting the given below expression. It is superb and combines binomial and hypergeometry.
Wolfram Alpha has genius computational intelligence to do these. Three cheers to Wolfram Alpha.
The expression is
I have typed the expression again in Microsoft Word.
Hope you like this expression.
Have a nice day !!
I am presenting the following expression today. This is a binomial expression. I admire Wolfram Alpha for its computational intelligence. I doubt whether even if I had a great mathematical prowess, I would be able to make the result.
The result is compact. The result is tidy and beautiful. Don't you agree, dear blog readers?
I have typed the expression again in Microsoft Word
Have a nice day !!
I was wondering a solution to 2n^2+2n-1=0. The solutions were 1 plus root3 by 2 and 1 minus root3 by 2.
They are great in continued fractions.
Now I am nearer to infinity
Now, in my earlier blog post I pondered on the expressions (mn+m-1)/(mn+m). I am definitely convinced that they can be considered to be of golden ratio. Moreover, I don't get comments against them. As a lone man possibly I believe in madness and Jesus allows me entitlement to my beliefs.
Now in this post I am asking myself is 1/(a/b - c/d) valid for infinite series.
As they are most beautiful and expresses the finger system; indeed these are valid.
However I realized that the Holy Bible is against this process of thinking of mine.
So clinging on to golden ratio and fingers system expressions are not wise. In fact it is foolish to do so. Guidance from you is expected.
Have a nice day !!
Infinite series is about convergence. To me. However, Ramanujan worked on divergent series too and has possibly come up with astounding results.
Imagine you are standing in a dark room with a torch light in your hand. If you switch on the light and sway around you see what is there in the opposite wall. The portrait of your late father. The statue of Shiva.
Now imagine you are standing in the same position with a flower in your hand and darkness everywhere. Now can you throw the flower on the portrait of your late father? Can you throw the flower on the statue of Shiva?
You may not be able to. Why?
Because of divergent behavior of the flower motion. And also, most importantly the absence of light.
I have convergence built in my system and so am able to see the portrait of my late father. So to say. Or the statue of Shiva. So to say.
If you think otherwise or if you have doubts or if you are not clear in the reasoning you can do so by commenting below.
Thanks for hopping in. Have a nice day!!
I had done these earlier in parts.
The expressions in constants are beautiful. Because they are of nature. I have done many expressions in constants. You can look at them by clicking on the Label Constants.
I earlier did expressions on 1, 0 and a few irrational numbers of the form root n. These are also very important as they give insights into shapes and geometry. But I was unable to categorize them and group them under one label.
Here in I am giving the expressions on root 2 and root3.
Root2
Root 3
I have about 40 to 50 original expressions, all made with the help of Wolfram Alpha. Wolfram Alpha has been a committed Internet master and I aligning with Wolfram Alpha have been able to streamline my own understanding of nature, nature's geometry and its symmetry.
I passed on my expressions to you also, dear blog readers. I hope you enjoyed the ride as much as I did.
Have a very nice day, dear blog readers !!
Euler-Mascheroni constant, gamma, now completely expressed in consecutive numbers.
Here is the Wolfram Alpha screenshot.
I have typed again in Microsoft Word.
I hope you like it.
Have a nice day !!
Special thanks to the Lord of Internet mathematics, Wolfram Alpha.
I have managed two more expressions combining golden ratio and Archimedes constant. They are
I have typed the above in Microsoft Word.
In total I have 3 expressions combining golden ratio and Archimedes constant. And one theory sorts expression combining golden ratio and Archimedes constant.
BHEL R&D department, here I come . . . . 😅😅😅
Have a nice day !!
I shall be doing drawings for comic artist. Comics are powerful media as one can tell stories.
But I realize accuracy has to be made a habit.
So I shall be correct. And try to accelerate on correct footing. Accurate triangles and appropriate quadrilaterals will be mantra in my approach to drawings in the next two quarters.
Happiness, cheers to my blog readers!!
Is mn+m-1 of golden ratio?
References
0,1,1,2,3,5,8,13,21,. . . . is of golden ratio. 1.61803
1+1/(1+1/(1+1/ . . . is of golden ratio. 1.61803
m^2-m-1=0 gives 1.61803 and -0.61803.
Points to think of
Slight variants to m^2-m-1 give golden ratios. For example m^2+m-1=0.
Other equations like m^2-2-1/m and their slight variants give golden ratios.
My stance
1.61803 and 0.61803 are important. g and g-1. Consecutive numbers sort.
There are two values to golden ratio. Instead of the quadratic expression m^2+m-1 , I have used mn+m-1..
What I feel like
It is appropriate to claim mn+m-1 is of golden ratio.
Three plans.
1. Become an above average comic artist. Lesser than Anupam Sinha!!
2. Learn Rudram. Shiva mantras.
3. Learn Malayalam. Family essentials to some extent.
I have downloaded necessary apps. But I don't know whether I can focus enough to learn above three. 😀😀😀
In history, man came up with 1,2,3 . . . .
The cooking and the agriculture historic man did realize 1 fertilizer to 3 water. Or 1 spoon of salt to 2 cups of rice.
The simplest rational number is 1 by 2.
What next ?
Golden ratio based is my answer. mn+m-1 types.
I am talking of ((mn+m-1)/(mn+m)-(mn-1)/(mn)).
If you beat me in above, I am willing to do anything you ask.
And if I beat you, then accept.
If Modi Government does Ikigai based HR policy . . .
If Modi Government appoints me for comics . . .
If I am asked to teach kids on comic art . . .
. . . then I will insist on accurate triangles technique and insist on Quality unit for triangle technique.
Trrrrrrriiiiiing . It is the alarm ...
I wake up. And it was a dream.
I need to learn digamma and Lerch transcendent theories. These are urgently needed to improve my scholarship and quench the thirst inside.
The reasons are
There are two drawbacks in my aim towards comic drawing.
They are
1. Great hands
2. Perspective of human figures with camera above head and at ground level.
Both these are due to foreshortening that happens. What is foreshortening? The below drawing will explain. Look at the two fists..
I hope to improve foreshortening with PDCA approach in days to come.
Edwards Deming PDCA shall be used for
1. Improve general quality of drawings
2. Improve foreshortenings
I have been using PDCA for improvement of general quality of drawings and there is improvement in drawings. I am happy.
However foreshortening is a different ball game. It is geometry. I have a theory that 4 sided geometric figures can be approximated. And not 3 sided. I shall use this theory along with PDCA and improve geometry and thereby the foreshortening base.
Anyone can use this theory and improve foreshortening.
Have a nice day !!
