47 drawings per day

You may be aware of my plans of becoming a comic artist.

You may have noted that the month of January will be for drawing hands; and from 17th onwards till 31st January I shall be learning outdoor perspective drawings.

Here I am outlining what I shall do from February 1st, 2024 till December 31st, 2024.

5 drawings of PDCA of human figure with camera at shoulder level.

5 drawings of PDCA of human figure with camera at above head level.

5 drawings of PDCA of human figure with camera at totally at ground level.

5 drawings of PDCA of one animal with camera at shoulder level.

5 drawings of PDCA of one animal with camera at above head level.

5 drawings of PDCA of one animal with camera at totally at ground level.

5 drawings of PDCA of human hands

5 drawings of PDCA of one object like car, train, computer etc.

5 drawings of PDCA of another object

2 drawings of outdoor/indoor perspective scene

So totally 47 drawings will be practiced per day. 

I am confident my drawings will be of high quality on January 2025. In 2025, I will start inking too.

In January 2027, I will go digital.

In August 2028, I will be retiring.

Have a nice day !!

New year plans

 

I have ordered the above book.

It seems a work of genius.  The author explains the process and steps too for drawing perspective outdoors drawing. 

The book will arrive on 17th January 2024.

From 17th January to 31st January 2024, I shall be learning from the book.

From 1st January to 16th January, I shall be practicing hands.

And from February 2024 I shall be practicing my PDCA of human, objects and animals. 

Have a nice day. !!

Yes I am aiming for comics on retirement. 

The world of golden ratios

About 15 years back, my seed of mathematics got to come out of soil with a few leaves exposed to the world outside. Measuring behavior, 22/7, Pythagoras theorem ideas were shared.

Later when alone a few years back, I began developing more on the above ideas. I got infinite series, constants, convergence, binomials, approximations and hypergeometry.

In particular was my form of expressions as shown below were explored to the maximum.

I termed them rational number series and also consecutive numbers.

In the last few days, I tried with an expression as shown below

After working on above form, I discovered that they are binomials.

The following results were obtained.

Also the Wolfram Alpha screenshots to confirm that the expressions are correct.

In the above, not only

are of golden ratios;

But also

I termed these world of golden ratios.

Have a nice day !!

For the new year

Naya saal aane ko hai, ke raaste bani hain hume chalna hi hoga

Nayi immaarthon ko soch aur samanvay se hume banana hi hoga

Golden Ratio and approximations

Golden ratio is the most beautiful thing in the world. 0,1,1,2,3,5,8,13, . . . are of golden ratio. It is like a man saying to the father in church. I am smaller than you. And the father gives a beautiful reply. I am smaller than Lord Jesus in the same proportion you think you are smaller than me.

Approximations are similar to golden ratio in some aspects. It makes the world beautiful. 

I feel possessive of the three approximations that I managed to make with the generous help of Wolfram Alpha.  You can look at them in case you missed them by clicking on the Label of this blog "Approximations".

Tomorrow is Christmas.  

Wishing all my blog readers a merry Xmas. 

Also I have ordered Dictionary of Mathematics from Amazon.  This Dictionary will be helpful in understanding "Theory of Complex functions" book.

My good wishes dear blog readers!!

National Mathematics Day

Today is the birth anniversary of Srinivasa Ramanujan.  December 22nd. Commemorated as National Mathematics Day. 

Ramanujan did work on Ramanujan Tau functions and Ramanujan Theta functions . These two are fundamental functions in Number Theory.  I have made blogs on above two.

Ramanujan is also known for two constants named after him.

Ramanujan worked on partition of numbers and he came up with some astounding results. 

Ramanujan did work on Mock Theta functions.  And these were his last work. 

He gave interesting puzzles too. His pi formula is among the fastest converging pi formulas of the world. 

Let all the mathematicians of India be inspired by Ramanujan.  Let them come up with work the world recognizes.  Let them be driven by intuitions.  Let them work with methods.

Let us keep the memories of Ramanujan. 

The rational number

 Below is the infinite series expression for the rational number p/q.

Hope you like it.

Also consider the following 

Hope you like this expression too.

Have a nice day !!

A Recursive Statement

 Given below is a recursive statement. And they are of consecutive numbers.

I hope you like it.

Have a nice day !!

Indian Problem Solving Ability

Indian Problem Solving Ability (IPSA) is a much desired quality by youngsters and not so young too. Some very old men too desire to have this quality when they should be focusing on attaining moksha.

Unfortunately IPSA has wrong foundation.  It is shocking that IPSA has wrong base. Water flows from low level to higher level without pumping. 

Photo of IPSA

Have a nice day !!

Consecutive numbers, golden ratio and Archimedes constant

The formula below gives the relationship between the consecutive numbers, golden ratio and Archimedes constant. Archimedes constant is also commonly known as pi. 

It feels great.

Have a nice day !!

The loose pictures

The pictures are there. Inside me. Loosely connected. Of the magnificent nature. The powerful nature. 

The pi

Its inverse and the golden ratio 

Hence the permutation,  the implied combination and the hour glass connection 

The permutation and gamma equivalence to consecutive numbers 

The consecutive numbers in Taylor series 

And the cos and cosh results. 

The above six are intertwined in my mind and body. 

It is him.

Have a nice day!!

To avoid confusion

Google blog readers may be confused as to what I mean to say from the Wolfram Alpha screenshots that I have been pasting in my blog posts.

This is what I mean to say. This is the final statement.

Have a nice day !!

These expressions are pretty good

The following expressions are pretty good. They are symmetric.  However,  one is coshx while the other is cosx.

Hope you like them.

Have a nice day!!

Hypergeometric distribution pattern observed again

One of the key ideas on blogging is to spread knowledge on mathematics to deserving young minds. 

Another pattern of importance was discovered yesterday.

And in this blog post I am sharing with my blog readers. It is of sigma 1 to infinity of n(n+1) divided by (mn)!. 

The results show interesting hypergeometric distribution. 

Hope you like the pattern and the expressions. 

Have a nice day !!

Does it encompass all?

Did Gauss saw it all? His advocacy of Complex functions.  Basically functions having complex arguments. 

I have the above book. But I feel one needs to understand German language to get into the groove and understand the nuances. Indian English will not be enough to get into the book. Because Riemann is very particular.  Very methodical. Very demanding. Very specific.  In the book.

Abel disagreed. And said that Quintic equations cannot be solved. The world says Abel is correct. Gauss rejected his work. 

I don't know how numbers are treated in far east. In Israel. In America. Forget Europe. 

Hume kya lena hai duniya waalon se? Roti milthi rahe. Bas itna sa khaab hai.

 Good bye. Have a nice day!!

Plus and Minus

 My expressions

Have a nice day !!

Being human

Being human is being oneself.  Myself.  Shiva is above us. Jesus is around us. But being myself is the way and the way the world understands. 

The number m, the e formula,  the cos and sine. The way I see them.

Have a nice day!!

These four screenshots

 I present the following four screenshots.

Hope you like them.

And these too.

Hope you like these too.

Also I would like to remind you of the following two formulas

The expressions above are great for finding the difference in differential of cos(x) and for finding the definite integral for a range of sin(x).

Have a nice day !!

A few lessons to me

Consider the following expressions 

I have used i, the complex number in both. 

One gives a simple cos(x) expressions.  While the other cosh(x). This is a discovery. 

Another point is, now I think I am in a position to get sigma integral equivalence for trigonometric and hyperbolic functions. 

Have a nice day!!

These expressions too on 26th November 2023

These expressions are hereby presented on 27th November 2023. 

Have a nice day  !!

This expression on 26th November 2023

Special thanks to Wolfram alpha.  

I present this expression today. Like many of the earlier expressions this expression too is on e.

Have a nice day !!