Pyramids of Squaring Pi.
The powers of Pi
Of ferman: Fernando Mancebo Rodriguez--- Personal page. ----Spanish pages
"Its special mathematical and geometrical properties and qualities define and place the Squaring Pi to be the correct Pi number"
You can see many of my works, in the following pages:
COSMIC and ATOMIC MODEL ||| Video: Cosmic and atomic model
Double slit and camera obscura experiments: ferman experiment ||| Type of Waves: Questions of Quantum Mechanics
The socurces of gravity. ||| In favour of the cosmos theory of ferman FCM ||| Theory of Everything: summary
Model of Cosmos. ||| Development speed of forces.||| Magnets: N-S magnetic polarity.
Stellar molecules ||| Static and Dynamic chaos||| Inversion or Left-right proof ||| Scheme approach TOE
Chart of atomic measures||| The main foundations of the Cosmos' Structure ||| Unstable particles in accelerators
Short summary atomic model ||| Positive electric charges reside in orbits.||| Mathematical cosmic model based on Pi.
Inexactness principle in observations ||| Einstein and the gravity ||| The Universal Motion ||| Atomic particles
Cosmic Geometry ||| Bipolar electronic: semiconductors ||| Multiverse or multi-worlds||| Light and photons
Quantum explanation of Gravity ||| Real physics versus virtual physics ||| The window experiment
Atomic Density ||| Linkin: Coeficients Lcf Mcf ||| Atomic nuclei structuring: Short summary
Few points about Cosmic Structuring.||| What is Time||| Simultaneity ||| The Cosmic tree ||| The Cosmic entropy
Interesting and short life of neutrons ||| Leptons field ||| Macro Microcosm, the same thing.
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
Type of Magnetic Forces ||| The big-bang and Universe' expansion ||| Astronomical chart: Astros, asteroids and microids
Certainty Principle: easy explanation ||| Certainty Principle and the Schrodinger's Cat ||| Wave function collapse
Relativity versus QM ||| The non-curvature of space by matter ||| The Master Clock
Ferman's light analysis ||| Cosmos basic elements, summary||| Comparative numbers in double slit experiment
Stars dimensions ||| Orbital situation of electrons ||| Bright cores versus Black holes
Summary of Ferman cosmic vision and models ||| Atomic nuclei similar to stars ||| Stationary time, but not local neither relativist
Neutrinos versus background radiation ||| Saturn says no to Einstein curvature.||| Da: Average density of energy in the cosmos
Gravity versus magnetic fields of force ||| Black holes cannot exist||| Expansion of materials by energy
Particles in accelerators: almost infinite ||| Trans-dimensional or ideal loupe||| 4D of space, time and matter
5D x 6D = Universal motion x time = Cosmic energy ||| The six cosmic dimensions
Neutrinos ||| Nature of light ||| Hydrogen atom ||| Uncertainty principle: test||| Criticism to Quantum M
Invariance Principle of Time ||| Stuffing forces and heat particles||| Physical waves and imaginary waves
Higgs fields and bosons: Imaginary elements||| Higgs bosons predictions||| Exotic particles
Stars as copies of atoms ||| ERF: Energy rebalancing forces||| Big Bang reality
Radial coordinates.||| Physical and mathematical sets theory. | Algebraic product of sets.
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
Transposition property ||| Accumulated product: Powers ||| Dimensional Geometry: Reversibility
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
Spherical molecules. ||| Genetic Heredity. ||| Metaphysics: Spanish only. ||| Brain and Consciousness. ||| Type of Genes T and D
Certainty Principle ||| From the Schrodinger cat to the Ferman's birds ||| The meaning of Dreams
Freely economy ||| Theoricles of Alexandria ||| Rainbow table of elements.||| Satire on the Quantum Mechanics
Cancer and precocious aging ||| Hardware and software of Genetics ||| The farmer and the quantum physicist
Dreams and unconscious logical computing ||| Intelligence and logic ||| How our brain and mind work
Andalusian Roof Tile. ||| Rotary Engine. ||| Water motors: Vaporization engines.
Triangular ferman's Houses .||| Pan for frying and poaching eggs ||| The fringed forest
Summary of Hydraulic Chenge Box ||| Ferman fingernails
The Emperor's new clothes and the QM ||| Garbage Triangle: Quantum mechanics, Relativity, Standard theory
Fables and tales of the relativists clocks.||| Nuclei of galaxies.||| Particles accelerators.
Hydrocarbons, water and vital principles on the Earth. ||| Cosmos formula : Metaphysics
Ubiquity Principle of set.||| Positive electric charges reside in orbits.
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
Chaos + symbiosis = evolution ||| Future Cosmology: Satire on Relativity and Quantum Mechanics
The stupid tale of the astronaut that did not age ||| Summary of Ferman cosmic vision and models
Climate due to human activity ||| Humans as herd animals
Video Universal Consciousness||| Who is God ||| Faces of God ||| Web Universal consciousness
Creation: Highlights||| First steps in metaphysics ||| A personal experience
Reason for the Cosmos' creation ||| The essence of life ||| Cosmic Entity: Metaphysics and Physics parameters
Pyramid of squaring Pi.
The Squaring Pi (proposed here as the right Pi number) consists of two parallel functions (exponential) of the inscribed and circumscribed squares to the circumference.
The pyramids of squaring Pi are numeric tables developed in pyramid or triangle form, which show us as successive powers of Pi go approaching to successive decimal powers of the inscribed and circumscribed squares to the circumference, to end up coinciding at certain level.
With the values of these levels of coincidence we can obtain the squaring Pi by means of root of these values.
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.
As we see, the odd powers of squaring Pi drive us to the inscribed square to the circumference, and the even powers drive us to the circumscribed square.
Here we observe as the Pi powers are approximately the double that the decimal powers (x10^n) applied to the perimeters of the squares, and it is due to get any decimal value applied to the sides perimeter is necessary the square of the number Pi (Pi^2 = 9.8696....)
We also observe that the powers of Pi in relation with the squares perimeters are the order of 2n+1 and 2n+2 due to for starting the pyramids of powers we need of +1 or +2 the powers of Pi to get the first term in the powers of the squares' perimeters.
Reasoning the number n of powers
The number of decimal powers n (10^n) that multiply the sides of the inscribed and circumscribe squares to the circumference is the number of powers applied to the triangles legs that form these sides when they are obtained by the Pythagoras theorem.
It seems to be that the coincidence numbers in powers (n=8 and n=16) for the perimeters of the inscribed and circumscribe square to the circumference are produced to this level due to these n-numbers are the numbers of times that we must to multiply the sides (legs) of the triangles to build the perimeters of the squares, as for the Pythagoras theorem.
Say, to form a side of the inscribed square (hypotenuse) it is necessary to elevate any leg to the square, what gives us as result 4 powers of legs for any square-side and 8 powers to the both square-side inscribed to the semi-circumference (Pi)
* For the pyramid of the circumscribed square the result will be double because of here it is not a semi-square, but a complete square.
(Summation of sides) x (summation of exponents on decimal-base) = (2 summation of exponents + 2) on Pi-base.
Other vision or geometric perspective is the alignment of the powers of Pi on the column of units.
This is gotten dividing the powers of Pi (Pi^2n+2) by 10^n, and with this we go observing clearer as these Pi powers go drive us to 8, the value of the perimeter of the circumscribed square to the circumference.
Getting this value (8) for n=16. (Remember, the number of powers that we must subject to the legs of the triangles component of the circumscribe square to the circumference)
The first idea for searching the Squaring Pi was born from the observation of the curve functions in the Cartesian coordinates.
If we look at the function y=x^2, this function gives us a curve, which in values between 0 and 1 is similar to a quarter of circumference.
So, if the perimeters of the inscribed and circumscribed squares to the circumference are straight lines, and the inscribed circumference is a curve, (having both the same basic parameters of construction: circumference diameter and squares sides), then it should be possible (and mathematically required) that adequate powers and roots of these perimeters give us any function that unites both parameters.
Later on, alone I must to practice and operate extensively till find the "Circle's squaring": The Squaring Pi.
Observation on the current Pi number
With the current algorithm method for obtaining Pi what we make is the addition of the semi-circumference points to build with them a straight line*, but Pi is an arc of circumference and not a straight line.
* Because here we are uniting and adding in a continue way the n-gon sides of the polygon in that we divide the circumference.
In this case, we forget a property or geometric principle that could say us:
"Any straight line that goes being curved endless, also goes losing dimension or longitude till disappear in a central point when this is curved indefinitely (endless) in symmetric or circumferential shape."
Say, any curved line has its corresponding coefficient of curvature, which in turn takes implicit a dimensional or longitude loss regarding the straight line.
And this is due to when we curve a straight line, the points that form the same go closing progressively among them by the interior side of the curve, till join together in a central point if the curvature is symmetric and endless.
Inversely, in the case of the algorithmic Pi, to the component points of the circumference we go adding them in straight line, and with that, we go extending them till form a straight line with more longitude (although in minimum value) than Pi in curved line.
And to finish, let me put the mathematical maxim of Squaring Pi.
* Mathematical maxim of squaring Pi. : "If the circumference is built, contained, limited and changed depending on the value of its inscribed squares (inner and outer), and vice versa...... Then, a direct function of the perimeters of these squares that gives us the exact value of Pi ought to exist, and vice versa ..... A direct function of Pi that gives us the value of the perimeters of the inscribed (inner and outer) squares to the circumference also ought to exist."
Proofs and Properties
Summarizing a lot, we can note the following properties and proofs of the quality of the Squaring Pi.
1.- Logically, the most important one could be the consideration of the Squaring Pi as de true value of Pi; although this question doesn't correspond to me its solution, but to the future mathematical development.
2.- The second characteristic is the easy way to obtain the squaring Pi by mean of two very simple functions of the inscribed and circumscribed squares to the circumference, say:
Pi = Raiz-34 de 8x10^16 ------------------- [8 x 10^16] ^(1/34)
Pi = Raiz-17 de 2-raiz de 2 x 10^8 -------- [2 x 2^(1/2) x 10^8]^(1/17)
3.- The third characteristic is the a lot of interrelations of all possible inscribed and circumscribed circumferences and squares among them that we can encounter expressed in different levels of the numeric tables of the Pyramids of Squaring Pi exposed in this work.
-- Inscribed square to the circumference = Circumference x (Pi^16/10^8)
-- Circumscribed square to the circumference = (Circumference x Pi^33) / 2 x 10^16
-- Inscribed circumference to a square = [2Pc x 10^16 ] / Pi^33
-- Circumscribe circumference to a square = (Pc x 10^8) / Pi^16
Where Pc is the perimeter of the square; and Pi is the Squaring Pi.
Taking in mind the anterior properties, coincidences and squaring of the powers of Squaring Pi in the building and structuring of the n-squares and n-circumferences inscribed and circumscribed among them in exponential way, properties that doesn't have the current Pi, I think the Squaring Pi has many possibilities of being the correct value of the geometric Pi.
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Direct formula for Pi: The Squaring Pi.