Friends, from time to time I go back to review some of my work and remember them in my groups.
Forgive me for being a bit heavy.
In this case I would like to talk a little about my ideas about the number Pi, and expose mine.
A subject to review is my vision of the total logical structuring of mathematics, and its geometric concepts.
For me, mathematics is a pure and strict logical norm, and therefore these requirements are always and everywhere met.
And with regard to the circumference and its "magic and elusive" number PI, it must also keep these principles of accuracy, mathematical logic, geometric logic, etc.
And based on these premises, I would like to distinguish my Pi number, (the squaring Pi) which I understand meets these requirements, from the current or algorithmic Pi number, which I understand does not meet the most important ones.

Let's see:
1.- The circumference is perhaps the simplest and most regular geometric figure, and therefore it should comply with the standard and logical/mathematical principle that: "all formulas for measuring and adjusting geometric figures are based on their structural parameters", ( such as radii, diameters, sides, angles, perimeters, hypotenuses, legs, apothems, etc.)
It is not expected that parameters or numerical values that are not in these parameters will be used to construct or measure the geometric figure.
That is, both mathematically and geometrically, the figures are composed, structured and measured by means of their parameters.
However, the current algorithmic Pi does not do it, but uses a series of values not connected to the parameters of the circumference, due to the fact that it seems that its results are getting closer to it.
Logically, and if the geometry and its numerical values are "serious and demanding" they should not give us the true final value.
However, my Pi number is based on a direct formula of these circumference construction parameters, mainly its diameter.
For this reason, I believe that my Pi number meets the first and obligatory condition, which is to be measured and adjusted with the values of its parameters (diameter).

3.- Another property that I have observed in the circumference is that it can be perfectly inscribed within a square, which is also defined and built (its side) by the same diameter as the circumference.
But it is also that, and from any circumference, we can go on inscribing and circumscribing other squares and circumferences to infinity, all of them being built and supported by the previous ones, that is, with the elements of some we build the structure of the others.
Well then, all these squares and circles circumscribed between them to infinity should have the property (circumscription theorem) that any basic element of this structure, and in the form of an exponential formula, has a formula that is capable of measuring and adjusting all and each of the elements of all these circumscribed figures, one above the others.
And yes, exponential formulas of my number Pi, they can give us all the measures of the elements and circumscribed figures. (Squaring Pi website)
But no, the current algorithmic Pi does not comply with this property, and if it is applied, it moves further and further away from the correct measurement.

4.- And finally, an observation or conclusion that I have obtained: Sometimes, many times, when I get a little bored I dedicate myself to "squaring circles", and I have observed that many of the possible segments and arcs inside the circumference "point to" the place where we have to place the segment Pi divided by 2, but they do not finish achieving their total accuracy, for which I understand that it is due to the fact that to find Pi, the basic parameters (radius, diameter, etc.) must be subjected to many roots and powers (for me the minimum root and key is 17, as is shown in this work)

As some of you say me to be interested In the philosophy and logic of my formulas to obtain Pi, because I summarize the foundations:
My idea and formulas for obtaining the number Pi consist of bending rectilinear parameters of the circumference (diameter, inscribed square, circumscribed square, etc.) by means of powers and roots of these parameters, until obtaining the appropriate curve of the number Pi.
In the drawing I show you a way of explaining it, where supposedly a larger square with side Pi is subjected to powers and roots until it becomes the square circumscribed to the circumference, and from here, doing the inverse operation we can obtain the number Pi.

Preamble:
For many years I have been surprised by the apparent persistence of the number Pi to "hide and evade" from a clear sample of its definition and mathematical demonstration through formulas that will show us its true value and situation.
However, and from this cyclical formula or function, my feeling has changed and my doubts have been cleared up and I understand that the number Pi has told us:
"Well here I am, imprisoned, located and measured by my own constructive parameters. Do you see me now"?

Friends, as already some of you know, I have my own point of view and proposals for the number Pi.
I understand that it have an irrational value, (but not transcendental) and that it is totally related, integrated and measured by the construction parameters of the circumference (diameter, inscribed and circumscribed squares, etc.)
During these years of considering it that way, I have been able to verify that it has more logical and with greater mathematical and geometric properties than the currently used algorithmic Pi.
Then, allow me to expose one of these peculiarities that I think is interesting, and would also represent a test of its validity.
It refers to what I call the Cycle of Pi squared, and which relates the square circumscribed to the circumference (8) with the number Pi of its inner circumference, and in which the decimal operative number (10) is used to maintain the level of operations (of powers and roots) close to unity, that is, at the level of the dimensions we are using.
This cycle function is simple, and as its name indicates, it is cyclic since the input result of the mathematical function is the same as the output result, if the correct Pi number is applied.
It is geometrically represented by a cycle or roulette on which we can rotate or maintain the circumference of the square of Pi, without it changing its value with the cyclic function applied to it.
Nevertheless, if we add a non-exact value of Pi to this loop, then the circumference of squared P is quickly distorted and destroyed.

Simplifying: The cycle would be like a tour in continuous rotation through a circle of value Pi squared, in which tour this value of Pi squared is analysed and "tuned" in each turn by the cyclical function exposed, in such a way, that if we have applied the correct value of Pi, the cycle and value of the circumference remain unchanged indefinitely.
But if the applied Pi is not correct, the circumference wobbles and destroys quickly: the faster the greater the error in the applied Pi.
In the same sense, with a variable of this cycle, and with a correct number Pi, we must measure (through powers and roots) all the squares and circumscribed circles on a first given circumference.

From my point of view, the currently used algorithmic number Pi is superseded and outdated by multiple tests and application of mathematical logic.
In other words, it is not acceptable in our time (in my opinion, of course) that formulas for obtaining and constructing the number Pi based on its construction parameters are not accepted, and yet continue to use an algorithmic series with the certainty that they are correct.
For me the evidence is compelling due to its quantity and clarity of application.
For example, the drawing that I put, as well as the video that I send you so that you can review it if you have time.
In the drawing, it is expressed that the relationship between the number Pi and the diagonal of its inscribed square (interrelation module) must be obtained from each other by mathematical logic.
If you observe this obtaining, you will see that the Pi quadrant that I expose does comply with these perspectives. Instead the algorithmic Pi fails.

Therefore and for me the question of mathematical logic that we should ask ourselves can be:
Can a false number (mine) unite, structure and interrelate with formulas all the construction parameters of the circumference, while the current algorithmic Pi cannot?

(*)In this diagram we see how all the circumferences and squares circumscribed on a first given circumference can be accurately measured by exponential formulas of the squaring Pi, and how the adjustment with the algorithmic Pi progressively deviates.

Here another simple way of obtain the Squaring Pi in function of its construction parameters.

And now the proof or revision of the Algoritmic Pi Inaccuracy.

Thank you