Cosmos mathematical model based on Pi.
URA, UMMA, atomic radii, atomic density.
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


Cosmos' mathematical model based on Pi.
URA, UMMA, atomic radii, atomic density.



During these last 40 years of my dedication to the cosmology mainly, and with the development of mi cosmic and atomic model, I was getting to the conclusion that the mathematical structure and architecture of the Cosmos is based mainly in the number Pi with opportune relation with the number 2, that to bi-dimensional level (area) it uses the form 2^1/2 (square root of 2) and to tridimensional forma it uses the form 2^1/3 (cube root of 2).
* Inclusive Pi has direct relation with 2, when it is possible obtain Pi by means of powers and roots starting from the number 2.
This idea was seem to be confirmed (and to be useful) when observing that due to the coincidence and approach of our decimal metric unit with the atomic measures, we could use Pi and the cube root of 2 for making structural formulas for atoms.
And some of these formulas are the ones expressed in these drawings.

Atomic density [HOTLIST]

At first, we can look at the atomic density,

D = Pi x Aw^1/2

- Where Aw is the atomic weight of the element to be considered.

At the beginning and measuring the dimension of the hydrogen atom I observed that if we adjust the atomic volume (4/3 Pi R^3 = 0,53467 x 10^-24 cm^3) y later the result is multiplied by the number Pi, this product gives us approximately the unit of atomic mass (proton mass).
0,53467 x 10^-24 cm^3 x 3,14159 = 1,6797 x 10^-24 g.
Later on, I proceeded to make the same operation with other chemical elements, getting the conclusion that when the square root of the atomic weights was included, the formula also gave me the atomic mass of these elements.
This way, I established the general formula that can be seen in the drawing, in which the atomic density of each element is given multiplying the number Pi by the square root of its atomic weight.
Da = Pi x Aw^1/2

General formula [HOTLIST]

As I said before, and following the physical formulas, the mass of one element is obtained multiplying its volume by its density. M = V x D.
On the other hand, we know the mass of any element is equal to its atomic weight by the unit of atomic mass M = Aw x amu.
So, from here we can draw the general formula in which we can include the atomic density, already expressed.

General formula:

Mass = volumen x density
Pa x amu = 4/3 Pi R^3 x Pi.Aw^1/2

And from this formula we can draw any other parameter, as the atomic radius of any element; the atomic mass unit, etc.
And so, we can draw also the atomic radius of hydrogen which, and as later on we see, it will be converted into the unit of atomic radius URA, very useful for obtaining the radii of the other elements in a simple form.

URA, unit of atomic radius

From the general formula before seen, we can draw the radius of the hydrogen atom, which will be converted into the unit of atomic radius URA, equal to 0,503523 x 10^-8 cm.
This unit of atomic radius URA is an interesting parameter, because the same than the unit of atomic mass, the URA can be used for finding the atomic radii of the other elements.
The formula that gives us these radii (R = URA x Aw^1/6) is getting multiplying the unit of atomic radius URA by de sixth root of the atomic weight of the different elements.
For example, and for the uranium R = 0,503523 x 2,49 = 1,2537 x 10^-8 cm.


R = URA x Aw^1/6

Differential of coincidence

A discovery (important for me) was when operating with these formulas I found an interesting coincidence or approximation:
If we look at the general formula, and for the hydrogen atom where the atomic weight is 1 and also its square root is also 1:

1 x amu = 4/3 Pi R^3 x Pi x 1 ------- amu = 4/3 Pi^2 x R^3

In this circumstance we can observe that:

Pi^2 x R^3 = 1,2599, that is approximately the cube root of 2 ----- Pi^2 x R^3 = 2^1/3

This way, here we can substitute the parameters Pi^2 x R^3 in the hydrogen atom by the simple and easy operation of cube root of 2, --- (2^1/3).
And this is very important because we have got the reduction a simples mathematical operations the general formula for the atomic dimensions.

UMMA, Mathematical unit of atomic mass [HOTLIST]

Using the simplification that gives us the differential of coincidence, Pi^2 x R^3 = 2^1/3, and applying it to the hydrogen atom, we can establish a unit of atomic mass UMMA totally mathematical, which will be:

UMMA = 4/3 x 2^1/3 = 1,6798 x 10^-24 g.

URA, using the differential of coincidence [HOTLIST]

Equally, we can obtain the URA (unit of atomic radius) using the differential of coincidence.

URA^3 = (2^1/3) / Pi^2 = 0,12766
URA = 0,12766 ^1/3 = 0,5035

Besides the explained data, many other coincidences and applications of the number Pi exist in the Cosmos' structure; some of them are exposed in the initial drawings and other ones in my atomic model.