#PythaShastri Complete Numbers

There are three observations when we think of numbers

1. Number lines have thickness (series of squares)
2. When we count with fingers we encounter gaps. And it is because of gaps that fingers are distinct. Similarly, trees and gaps between trees.
3. In every day encounters we say 4 cows are going inside shed; 2 cows are coming out of shed. In other words positives and negatives.

Complex numbers were invented to take care of all these and more. Euler was not aware of complex numbers but belonged to an era earlier to complex number invention.

#PythaShastri had written about the e series. The fingers and the gaps. #PythaShastri had also written about 1,2,3,4,5,9,10. The hour glass. The folding of paper. The visible sides being 1,2,3,4,5 and we halve by going from 9 to 10. So 1,2,3,4,5,9,10. But 3,2 to 4,5 was not discussed in full.

Here, I am discussing 3,2 to 4, 5.

3,2 to 4,5 if included with 1 make a complete hand. 1,2,3,4,5. Also 2 to 4 is doubling. 2 to 4 is squared. And 1 to 4 is four times. The reverse is one-fourths.

If we take the 2 to 4 squared and 1 to 4 is one-fourth, then we get square series of natural numbers..

Consider squares of even numbers,

4, 16, 36, 64, 100, 144, . . . . .

The one fourth of above is

1, 4, 9, 16 ,25 ,36, . . . . .

or

1 ², 2 ², 3 ², 4 ², 5 ², 6 ², . . . . .

This demonstrates that 3,2 to 4, 5 is a natural phenomenon of square series.

Continued Fractions

Continued fractions are interesting and are considered important in constants and irrational numbers.
I have a good interest in continued fractions.
Continued fractions require great imagination and arrangement thinking.
I have understood the continued fractions for root 2, root 3, phi and pi.
Khinchin constant is on continued fractions.

Indo Asian hour glass

I had developed the equation for sa, re, ga, ma, pa, dha, ni. The equations were :-
1 + t
1 + t squared
and
1 + t cubed.
In a range of 1 to 10, the equations gave me the importance of numbers 2, 4, 5, 8, 9 and 10.
When we fold a paper we get 1, 2, 3, 4, 5, 9, 10. This has already been explained.
It is clear from the two sets of numbers that my timing is musical. 2 raised to the power of 1 by 12.
Hence Heegner numbers are not easy.

Heegner numbers

Heegner numbers are what I am interested in. But I plan not to go further. Because it is beyond me.
Ramanujan knew about Heegner numbers. And therefore my curiosity is a subset of his knowledge. That's the way I prefer to view my mathematical endeavours.
I have many ifs of past life. Opportunities that wasn't there. Opportunities that I just missed. But I'm confident. Just one correct friend and I can change for  better. That's the way I feel in the present.

Alternate Lines

Alternate lines are a new idea .
This is to represent folds in clothes.
This was the last challenge in cartoons.
I have conquered this challenge in my own way.
How is this idea?
I mean, how much percent is it effective vis a vis folds in clothes.

If I were to improve sports ability . . .

If at this age, suppose I want to improve my sports ability of mine, what would I do?

1) I would believe in strength/fat=athleticism equation.
I would increase strength and reduce fat both at the same time. This will give me the most benefit. I believe it should peak my sports ability by about 66% or more.

2)I would believe in #PythaShastri Second max reps is half of first max reps.
I should know whether my strength is increasing. I will do two sets with a heavy dumbbells for all of my body. Suppose the first max rep is coming out to be 12; then, I will strive to go beyond 6 in my second max rep.

3)I would eat palm sized protein helping in every meal.

4)I would synchronize my breathing and my legs.(#PythaShastri method)
Be in a standing position. Breathe in. At the same time sway right leg in clockwise semi-circular arc from front to back. Breathe out. And at the same time sway right leg in anti-clockwise semi-circular arc from back to front.
Then do the same for other leg.
(The angles in a semi-circle is 90 degrees fundamentals are being used here.)

5)I would do squats more.

6) I would do heel raises.

7)I would do pranayama.

But I have become old. And I can do running only with my brain being conscious all the while.

Cartoons Improvement

These are the things I am doing to improve cartooning and caricatures.
In caricatures, I am learning to use pencils and erasers effectively.
Mandolin U Srinivas it is supposed to be. Forgive me for non resemblance.