A hint of the Gauss constant

I wrote earlier why 1.414 .... And not 0.414... So also for why 1.732.... And not 0.732.... in my "The other day" blog.
Below I present 2 screenshots. First is the continued fractions of
 1+ 1/(root(2)+1/(root(3)+.....
The second is 1.53... divided by 0.8346 which is the Gauss constant. The result is 1.83....
So in a way I have shown why 1 is added. Using Gauss constant.

How about this ?

(It is a privilege to see Gauss constant. Gauss is really too good and very high. Gauss is considered the greatest mathematician by many guys over internet. He won the Copley medal too. Wow !! I feel honored to see Gauss constant...... though partly !!)

I feel there are many criticism on 0.8346 and 1.8346 results with continued fraction of the type root (n). 

Why it is not accurate? 

It is not meant to be. Ceiling and floor are to be used.

My result demonstrates the enormity of the Gauss's constant G. It includes the explanation of initial value in continued fractions and also the ceiling and floor functions.

In fact 0.8346 and 1.8346 result is as beautiful as 22/7 of pi.

Tilted Heads

Drawing a tilted head was a major milestone for me. Now, I have gained some confidence in drawing them. Andrew Loomis book has many tilted heads drawing. But they were difficult to practise. Now, I am reasonably okay with them.
You may be aware that I have two books written by Andrew Loomis. Both of them hard bound. They are "Drawing Heads and Hands" and "Successful Drawing". These books are really great. Andrew Loomis has so much to write about. It is amazing. Of course, his drawings are just superb and he is a great teacher.
His quote "To learn to draw is to draw and draw and draw" stresses how important it is to keep drawing. I owe the 3d look in my caricatures to the teachings and method of Andrew Loomis.
I shall be drawing :-
1. More and more and more faces and tilted faces till I get accuracy and humor vis-a-vis a real face.
2. More and more and more hands till they look convincing.
3. More practices on perspectives.
4. More practices on light and shading.
All the above with pencils/ charcoal pencils. And the methods of Andrew Loomis.
Till then, here is wishing all the best to my blog readers.

Thanks Brustro

Caricatures with charcoal pencils are enhanced when one uses Brustro kneaded eraser and Brustro blending stumps.
Look how smooth the shading becomes and how improved the caricature becomes:-

Exercises planned

There are health issues with me.
I decided to do 4kg dumbbells clean and jerk. And leg cycling. I am planning to do this everyday.
I counted and recorded leg cycling max reps today for 3 max reps rounds.
1
1/2
3/4 × 1/2
The below were assumed
4/5 × 3/4 × 1/2
5/6 × 4/5 × 3/4 × 1/2
. .  . .

Adding them all up for uptil 9/10 × 8/9 × 7/8 × . . .1/2 gave me 3.14.( I ignored 2/3 in all).

Raghu Rai & selfie

Ayodhya Issue

Today an issue has been raised as to whether Ram temple can be built on Muslim graves. A few individuals posed this question to Ayodhya trust.
Well, there are parihaarams and Hindu rituals like shuddhikarans and all. My answer therefore is yes. Our prayers start with cleansing. And later the names of God are taken. As far as my understanding and science-hinduism knowledge goes.
There were solutions like sharing the plots among three trusts and all. I wonder what happened to that judgement. Possibly a lower court judgement or something. But this judgement (sharing the plots among three trusts) would have given authenticity to quota based reservation. I am for quota based reservation.
I hope sanity prevails and the right justice is given to the Ram Janmabhoomi issue.

Ceiling and Floor functions

The ceiling and floor functions are very important. Floor(3.23) =3. Floor(3.5)=3. Floor(3.67) = 3. And Ceiling(3.23) =4. Ceiling(3.5)=4. Ceiling(3.67)=4.

Ceiling and floor functions are natural. A human has ceiling and floor functions built inside him.

If we say x = 10/3; then it will take millions of pages and still a man will be writing 3.33333 . . . . . But a ceiling and floor function prevents this.

A ceiling function or a floor function makes us say confidently π is approximately 3.14.

The rational number series contains equal to sign. This equal to sign has to be seen with the ceiling function or a floor function in the hindsight. Only then can it be properly appreciated. 

There is one prime number generator called Mills primes. The formula is μ^(3^n).

The floor of this function is always prime. This teaches us the lesson that ceiling and floor functions are nature approved and nature supported.

The crucial difference

Colin Maclaurin gave the formula
1/(1-x) = 1 + x + x*x + x*x*x + . . . .
Carl Gauss too supports the above from his formula for sum of infinite geometric series.
Then, I wrote
1/(n-1) = 1/n + 1/(n*n) + 1/(n*n*n) + . . . .
In the first case putting x as 1/n will make the left hand side equal to the right hand side.
In the second case n is meant to be positive integer for the left hand side to be equal to the right hand side.
Colin Maclaurin and Carl Gauss were telling us about the truth of nature and the world.
I was thinking of positive integers.
There is a small but a vital difference in the two.
And the crucial difference is complex functions.
I wrote about Ramanujan theta functions being the product of two difficult to quantify things like conscience and quality. I wrote it is up and working. I also wrote that there is no two. As no two things are similar. Things like these are the crucial difference.
The masters like Colin Maclaurin and Carl Gauss are perfect. We need to follow them.
And I need to make complete statements. Like
1/(n-1) = 1/n + 1/(n*n) + 1/(n*n*n) + . . . . are of positive integers.
Stephen Hawking wrote "God created integers". To me integers are creations of God, then.

Charcoal

Expression for π/8 and more . . . .

Here in I am presenting an expression for π/8. This is a new type of expression. And is quite an interesting one. the reason is this. The expression in n/(2n(2n-1)) and is alternated with + and - from 0 to infinity. If the expression is made (2n(2n-1))/(3n(3n-2)(3n-1)) or further to (3n(3n-2)(3n-1))/(4n(4n-3)(4n-2)(4n-1)) or further to (4n(4n-3)(4n-2)(4n-1)) /(5n(5n-4)(5n-3)(5n-2)(5n-1)) and so on the expressions are of pi. 

How about that for some beauty? It is a wow!! The brilliance of π. The brilliance of Wolfram. And a slave, myself. All together in the glory of God and nature.