The Squaring Pi Theorem

The Squaring Pi Theorem
Of ferman: Fernando Mancebo Rodriguez--- Personal page. ----Spanish pages

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Hello friends, allow me to start by setting up a small postulate:
"Pi is an exponential and cyclic number, which means that cycles of powers of Pi can adjust and measure all other parameters of the circumference."
And with this we can establish a slightly broader theorem, which would be:
"All the parameters of a given circumference (r=1), as well as all the parameters of its squares and circumferences inscribed and circumscribed on it, till infinity, can be adjusted and measured by means of powers of the Squaring Pi, with application of a decimal reduction coefficient (10^n) to place the value of the searched parameter at its appropriate level".
For example:
Pi^34 = 8.10^16, and therefore being the squaring Pi= 3.14159144414199265........
Where 8 is the square circumscribed to the circumference, and 10^16 is the decimal reduction coefficient.

Logical philosophy of Pi: geometric and arithmetical similarity.
Similar to how geometrically the circumference represents a closed cycle inside and outside of which its construction and composition parameters are redistributed (radius, diameter, inscribed and circumscribed squares, etc.), equally arithmetically the number Pi is constituted in cycles or circuits of powers that measure and analyze all these construction parameters.
Measuring the first cycles to the parameters of the base circumference, and having and constructing cycles of Pi bigger circumscribed to these that are measuring the circumferences and circumscribed squares, that is, an arithmetic behavior similar to the geometric structure.
In this sense, it is not a transcendental number or value that tends towards a straight, indefinite and invisible horizon, but also arithmetically transforms into well-defined cycles around a central point.

* Dimensional loss when bending the straight lines.
"Every straight line that curves has a dimensional loss of length when all the points on the interior of the curve approach each other, and vice versa."
In the same sense, both the sum of the sides of the polygons inscribed in the circumference and the series produce us straight lines, and with that, with minimal increase of length.

* In the following diagram, we can see how power cycles of Pi can give us all the squares and circumference circumscribed between them to infinity (applying the appropriate decimal reduction), and how the current algorithmic Pi cannot.

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* The mathematical (and perhaps philosophical) reason for the application of a decimal reduction in the powers of Pi is that the peculiarities of the decimal system make the high powers tend to take enormous values, when what the number Pi needs is that the cycles of powers that maintain values close to unity, an issue that is solved with the decimal reduction, (that is, without moving away from radius 1 that creates the parameters of the circumference).

The cycle of Pi Squared

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Meaning in brief:

"The Pi squared cycle is a circuit or mathematical cycle to verify the accuracy of the number Pi that we apply.
Geometrically we suppose that we make circulate the value of Pi squared (little ball in the roulette wheel), increasing exponentially in each turn the possible inaccuracies of this value, in such a way that if the applied Pi is exact, the circuit remains invariable; but if the applied Pi is not accurate, the circuit will wobble and be quickly destroyed."

The Pi Squared Cycle: Roulette or Pi Trap.

Accuracy test.

Preamble:

For many years I have been surprised by the apparent persistence of the number Pi in "hiding and escaping" from a clear sample of its definition and mathematical demonstration through formulas that 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 and I understand that the number Pi can tell us:
"Well, here I am, enclosed, located and measured by my own construction parameters. Do you see me now"?
Friends, as some of you already know, I have my own point of view and proposals for the number Pi.
I understand that it has 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 like this, I have been able to verify that it has more logic and with greater mathematical and geometric properties than the algorithmic Pi that is currently used.
So let me present one of these particulars that I find interesting, and that would also represent a proof 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 operating decimal 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 the name implies, it is cyclic since the input result of the mathematical function is the same as the output result, if the correct number Pi is applied.
It is represented geometrically by a cycle or roulette on which we can rotate or maintain the circumference of the square of Pi, without its value changing with the cyclical function that is applied to it.
However, if we add a non-exact value of Pi to this loop, then the circumference of P squared is quickly distorted and destroyed.
Simplifying: The cycle would be like a tour in continuous rotation around a circle of value Pi squared, in which tour this value of Pi squared is analysed and "tuned" or (increased in error) at each turn by the function exposed cyclic, in such a way that if we have applied the correct value of Pi, the cycle and the value of the circumference remain unchanged indefinitely.
But if the applied Pi is not correct, the circle wobbles and is destroyed quickly: or faster, when 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.

Demonstration and Testing

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As we can see in the drawing, the effectiveness of this Pi squared cycle is very high, since although the algorithmic Pi currently used is very approximate, when we submit it to the Pi squared cycle test, already for the fourth return to the cycle is destroyed and out of the loop.
And if we use only the approximate value of Pi = 3.14, the value of the cycle (Pi^2) is destroyed in the first loop.
On the other hand, the Squaring Pi remains intact, which in my point of view is a clear demonstration of its validity.

Some examples

Next I put drawings of how to use the Squaring Pi cycles to obtain simple parameters of the circumference; although they can be extended to obtain values of all the squares and circles circumscribed between them.
Likewise, some curious examples such as the Squaring Pi Pyramids.

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In this second pyramid, it is shown the power Pi^34 in relation with the perimeter of the circumscribed square to the circumference (8) by the decimal powers 10^16.

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Fourth dimension of space.||| The way to get a unity theory||| UHECR Ultra-high-energy-cosmic-rays
Magnetic or entropy forces: types or classes||| Time observation and time emission ||| The universe expansion
Planetary Mechanics : Short summary ||| Easy explanation of the Planetary model||| State and type of Particles
Higgs boson and fields: wrong way ||| The positron proof: main types of magnetic fields ||| The gravity proof
Current state of cosmology ||| Electromagnetic charges: reason and procedure ||| Neutron: The short and interesting life of
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Planar angles: Trimetry.||| Fractions: natural portions.||| Cosmic spiral ||| Inverse values of parameters and operation
Equivalence and commutive property of division. ||| Concepts and Numbers. ||| Bend coefficient of curves ||| Mathematical dimensions
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Priority Rule in powers and roots ||| The decimal counter ||| The floating point index ||| Paradoxes in mathematics
Direct formula for Pi: The Squaring Pi. ||| The pyramids of Squaring Pi. ||| Functions of Pi ||| Integration formulas Pi.
Squaring the Circle ||| Cocktail formula for Squaring Pi.||| Orbital coordinates in motion: Summary
Oscillating function: Cartesian oscillators ||| The ciclo as unit of angular speed ||| Squaring circles ruler and compass |||
Video: Squaring circles ruler and compass ||| The number Phi and the circumference.speed |||
The The extended Pi ||| Angles trisection||| Squaring the Circle regarding Phi||| Video of the two squares method
Discusion about the Pi as transcendental number|||: Not transcendental Pi||| The chained sets|||
Properties of equalities in limits||| The Phi right triangles ||| Pi and the Circumscription Theorem
Pi triangle by squaring the circle : Vedeo Pi triangle ||| Squaring Pi demonstration by circumscription Theorem LatexPdf
Doubling the cube ||| Framing the circle ||| Phi and Pi: relation formula
Squaring circle with Phi (to 0.000005 of ideal ruler and compass)||| Sbits: Static and dinamic orbital coordinates
Squaring Pi and the Floating Point ||| Planetary Vitality: formula ||| Sign of Simultaneity or coincidence
Squaring the circle by doubling the cube. ||| Video: Squaring and doubling. ||| Video: Squaring with two inscribed squares
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Chaos Fecundity. Symbiosis: from the Chaos to the Evolution.||| Speed-Chords in galaxies.
The ancient planets Asteron and Poseidon.||| The man and the testosterone.||| Toros say ||| The essence of life
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Creation: Highlights||| First steps in metaphysics ||| A personal experience
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Metaphysical nature of the Cosmos ||| The Man and his cosmic integration ||| Science versus Religious Faith
Vital Necessity of the Cosmic Entity ||| Creativism: nor creationism, nor determinism

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