+++++++

I have achieved it. Thank you Prof. Hussein Al Bahadli.

The concept described involves finding an "equilibrium" point in a model where self-efficacy, possibly linked to economic output or efficiency, is maximized. Here’s an interpretation of each part in mathematical terms:

Profit Margin and Input Percentage

A gross natural profit margin of 7.06% with a 44% input suggests that the model predicts a certain "natural" or maximum achievable profit (7.06%) when 44% of some resource (like capital, effort, or another measurable input) is utilized. This could be framed as a relationship where increasing input leads to diminishing returns, stabilizing at an upper threshold of 7.06% for profit margin with the 44% input.

If we consider:

P = f(I)

where

P

is the profit margin and

I

is the input level, the function

f

might be structured to reflect this maximum:

\lim_{I \to 44\%} f(I) = 7.06\%

Pi Division and Equilibrium Interpretation

The division of π (approximately 3.14159) by 7.06859056 to yield approximately 0.444444 might be aimed at finding a certain ratio or constant that represents "equilibrium" within the model. The result:

\frac{\pi}{7.06859056} \approx 0.444444

may imply that this ratio has significance within the model as a balance point. Mathematically, this suggests that the ratio of π to 7.06859056 approaches a value close to 0.444444, which could be viewed as an equilibrium constant or a specific point where certain model conditions are balanced.

Possible Interpretation in a Libertarian Model of Self-Efficacy

If we consider the model as representing self-efficacy per capita, the ratio of π to 7.06859056 might symbolize an ideal or "natural" efficiency ratio per person in a system where individual contributions stabilize at a certain efficiency level. This ratio might define the optimal balance between input and output, representing a point where increasing input beyond 44% does not significantly increase the profit margin beyond 7.06%.

In Summary:

The numbers and ratios provided suggest that the model reaches a form of equilibrium at 44% input, where the output (profit margin) naturally caps at 7.06%.

The π/7.06859056 ratio yielding 0.444444 could represent a natural efficiency ratio, implying that in this equilibrium, individual or system-wide efficiency stabilizes at this value per unit of input or effort.

This approach suggests a model governed by diminishing returns, where after reaching an optimal input threshold, additional input does not substantially increase output, which is a common concept in economics and efficiency models. Additional context on the specific field or purpose of the model would help refine the interpretation further.

How do you define superrational?

Connecting geology with astronomy.

I mean pi is related with embeddedness of planets in the solar system.

Thanks. Probably not something that I can help with then I'm afraid. Certainly pi is irrational in a mathematical sense, but I presume that this does not contradict it being superrational in your sense?

I only need help to publish my monograph. 7 pages not much.

Please let me know what you have understood and meant by 'help'.

1. If you extract pi value from a perfect circle - you will just have an approximation, however if you work with a natural ellipse - then superrational pi you will get.

2. If pi is indeed irrational, then one should explain why these pattern exists in its layers.

Dear Prof. Can we communicate per email?

Hi Ibrahim Usta By help, I mean helping to answer the question whether pi is 'superrational' - since you want to connect geology and astronomy, and I know neither of these subjects. From the mathematical point of view, remember that irrational does not imply that it does not contain patterns. Plus, if it were a rational number, this would make its pattern rather dull, as it would eventually end up terminating or just repeating itself in a cycle - being irrational makes it far more interesting!

By the way, one thing that you might enjoy is the beautiful patterns present in pi as a continued fraction (see this webpage for example https://mathworld.wolfram.com/PiContinuedFraction.html)

Dear Professor Thank you for explaining such traits about irrationality. However, this fraction found in a division layer of number pi, makes me suspicious about the concept of precision. I mean if we increase the number of decimal extension towards millions (as significance), or say billions then divide it with this (π÷7,06859056) then it seems more likely that the result will come closer to .4444444444444443999n" would this be categorised as a (almost) dull pattern? And I would like to know if this scenario in my mind about getting this pattern is viable or justifiable? Thanks for the link, I will try to internalize these depictions with my contribution. By superrational what I mean more precisely is that all the time on-going seismological events in different magnitudes might be aligning with (rationally) number pi's decimal properties in its layers. Since elliptical systems connect superrationally due to the interaction of three universal powers - solar energy (heat/light), electro-magnetic power and nuclear/atomic energy [no gravity because it is more specifically the end result, not an initiator] seismological events as all the time breaking of fault lines and volcano explosions - superrationally might be connected with the patterns of planetary motions and their aspects with each other due to their embedded elliptical nature peculiar to emergence of number pi.

Dear Professor Tuite please see this discussion with Grok AI machine, I thought maybe I am using a wrong term for my hypothesis "superrational" this probably makes the issue sound like a pseudo science. We can possibly make use of this feature in number pi for better precisions in life sciences. Thank you again.

https://x.com/UPrious/status/1878896596198498808

I have understood I was wrong but not exclusively.

Hi Ibrahim Usta

You certainly can find a constant c such that pi/c = 0.44444... (or any other number that you desire in fact) with decimal beginning c = 7.06858347... (this will be a transcendental number). But does this not 'transfer' the complexity to the constant c? That is, you can get as long a string of 4's as you like, but the constant c will in turn get more and more complicated.

Thank you this is great! I wish I could be a polymath by formation. I can't answer the question because I have not yet studied advanced math. I do not how they gather algorithms.

How can I take pi with a million decimals? And ÷7,06859056

You can find the first million digits here: https://www.piday.org/million/

What do I need to have while dividing it? ÷7,06859056

Probably you don't need that many decimal places? I mean, you're not going to read all of them I assume, unless you have a lot of patience :D You could try this site for example, which will give you more decimal places than an ordinary calculator: https://www.mathsisfun.com/calculator-precision.html (just picked this one at random, lots are available on the web)