* Squaring the Circle and Doubling the Cube *

Of ferman: Fernando Mancebo Rodriguez---
Personal page. ----Spanish pages

You can see many of my works, in the following pages:

PHYSICS:

COSMIC and ATOMIC MODEL |||
Video TOE, Simplified: II Physical vision

Video TOE, Simplified: I Metaphysical vision |||
Video TOE, Simplified: III Cosmic particles |||
First 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 |||
Big-boom instead Big-bang

Genzel and Ghez observations on galaxy center |||
Maxwell demonstration on charges and electrons situation

Orbital distribution positive charges (+) arises into Everything Theory|||
Ferman cage |||
Wave function collapse

Universal motion and its parameter: Time |||
Fallacy in the Uncertainty Principle |||
Brief study on the magnetic forces

The hypothetical ideal (Ubiquitous) observer |||
The neutrino test |||
Imaginary tube funnel deformation

The cosmic levels |||
The Universal Space-time constants |||
Energy, matter, mass, gravity, magnetic forces -->>>
Video:

The reason of electric charges |||
Weak electromagnetic forces|||
Standard Model versus ferman toe 1992

Relativity is wrong: only forces move particles |||
Stellar molecules, but no black holes

MATHEMATICS:

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 |||
Planetary Vitality: formula |||
Sign of Simultaneity or coincidence

OTHER:

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

Multiverse: multi worlds |||
Biological and Psychological sexuality |||
Genetics: types, aging, sexuality

INVENTIONS:

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

ARTICLES:

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|||
James Webb telescope: predictions

Vectors and fields of forces |||
Evolution versus Superposition |||
Systems of multiples suns

METAPHYSICS:

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

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

Email: ferman30@yahoo.es

* Squaring the Circle and Doubling the Cube *

* Fernando Mancebo. April 1, 2023 *

Friends, I am going to expose this resolution of the squaring of the circle, for which it will be necessary at the same time to solve the other problem of doubling the cube, since for this squaring it is necessary to apply the segment cube root of 2.

However, we will first proceed to squaring the circle by applying the cube root of 2, to study, adjust numerically and better understand the squaring procedure.

Then, at the end, the extraction of the cube root segment of 2 is put, to build the squaring of the circle in practice, with a ruler and compass.

As seen in figure 1, the squaring will be carried out by means of the construction of two squares inscribed in the circle, which must be properly aligned to achieve the 8 anchor points (yellow), which together will give us the side (Sqrt. Pi) and wanted square (blue).

The theory and mechanics of drawing is very easy and simple to carry out.

As we will see, used square root of 2 to build the squares inscribed in the given circle; and we use the segment cube root of 2 to align these two constructed inscribed squares, and mark the anchor points for the final square of the quadrature.

In this first drawing of figure 2, we expose the initial circle to be squared with its various diameters (4), and then we mark the first inscribed square.

In this drawing Fig.3, we transfer the cube root segment of 2 (A-c,), previously obtained, over the center c, and then with the compass we make an arc until cutting the square inscribed in c'.

And we proceed to draw the line A-c'-p, which will mark the first anchor point p1.

Note.- For a better adjustment (especially mathematical) we can take the arc c'-p8, to mark the initial point p1. of the second inscribed square.

Now, Fig. 4, we proceed with the compass and square root of 2, to mark and draw the second square starting from the previous point found p1, and marking the other three points of the square p3, p5, p7.

And finally with the rule, we unite and extend the anchor points properly as shown in figure 4/2 to build the desired square of the squaring of the circle.

* In the following drawing some parameters and values of segments and angles are provided.

* Doubling the cube to get cube root of 2 *

* To double the cube, it is very convenient to use a compass with two very fine needles to be able to fix it well to the paper and so that it does not slip in the measurements and turns.

To double the cube, we have the following parameters:

1.- Firstly, the radius = 1 of the circumference and its diameter 2, whose cube root that we seek is 1.259921...

2.- Secondly, and starting from the principle (A) of the diameter of the circumference, we draw a chord of circumference C (Section AB, which in drawing practice, and to facilitate the work, will be replaced by the ruler fig. 2).

3.- Immediately we see that this chord C has its projection on the diameter in the segment (p), which forms the third element necessary to find the cube root of 2 (C).

Well then, if we observe and work with two of these three elements, the chord (C) and its projection segment (p), we build a formula that is basic and essential for our research: C x p = (from 0 to 4)

But pay attention! When this formula ( C x p) gives us the radius of the circle 1 (C x p = 1, third element), then we measure C and see that it is exactly the cube root of 2, that is, the segment we were looking for. (1.259921... x 0.79370052.. = 1).

Therefore, we already observed that there is an interrelation or quadrature by means of segments and formulas between the radius (or diameter) of the circumference, with a cube root of 2, and its projection on the diameter.

At this point we can already begin to feel some restlessness and intrigue:

Will we be able to obtain or "hunt" the elusive segment C, that is, cube root of 2?

Well, let's not worry, the answer is yes, even fun to do.

But, how to do it?

Well, using the component elements of the previous formula, C.p = 1, but using ruler and compass instead of numbers and quantities.

- The chord segment will be replaced by the ruler with which it rests at the beginning of the diameter (A) until cutting the circumference at point (B).

- The projection segment on the diameter (p) will be used as an arc (arc p) that will intersect (arc.r)

- The radius (1) will be used to create another arc of connection and measure (arc.r) that will be the unit of measure and future side of the cube to be duplicated. Next Fig. 3

In this section we should already forget a bit about the measurements and numerical verifications: Let's take the compass and the ruler, and proceed to draw on a circle of radius 1, with its centre and diameters already marked.

- The first thing to build is an arc of radius = 1, (with centre at point A) and from the centre of the circumference to the left, which serves as a guide, measure and support for the other two basic elements that we are using.

- Now, we take the rule and at the beginning of the diameter (point A), we cut with it the circumference at the test point (B), creating a space or segment from this point to the vertical diameter.

- To this segment or distance (a-a'), we measure it with the compass, and we translate this measurement on the horizontal diameter creating the segment (a-a'), at which point (O) we begin the verification of the confluence of elements with the compass.

Logically, the first tests will fail and there will be no coincidence between the rule and the cut between the arcs, (cut arc r - arc p).

So we move the ruler in the right direction and try again the squaring or confluence of elements.

By moving the ruler in the correct direction and carrying out the above checks, after 3-5 attempts, the quadrature will have been achieved and we will be at the point (q) of confluence of these three elements.

At that time, we mark point B on the circle and we can definitely draw the segment AB = C which is the cube root of 2.

As we have seen, to square the circle we need the cube root of 2, and therefore we must first find this segment (cubic root of 2)

However, this double process results in the discovery of two unknown properties of the circumference, and therefore a good contribution to the knowledge of this geometric figure.

Doubling the cube:

The first (by doubling the cube) we discover that there is a hidden parameter in the circumference, which is the cube root of 2.

And I call it hidden because to discover it is necessary to do it through mathematical operations.

This parameter or segment (C) inscribed in the circumference consists of a chord of the same, which if we multiply it by its projection on the diameter (placing on one of the cuts of this circumference chord) gives us its radius 1.

And then we will see that this chord or segment measures exactly the cube root of 2 (1.259921.....

Therefore finding this chord we find the cube root of 2.

And as we have seen in the previous explanation, it is very easy to achieve by means of a single expert measurement with the compass.

And I say expert because the better we know how to handle the compass and the greater its reliability, the faster and more accurate the measurement will be.

However, and as we have seen that the method is correct and exact, the process will also be correct and exact.

Squaring the circle

In squaring the circle we also discover another (until now) unexpected property or characteristic of the circumference:

And it is that the cube root of 2 is mathematically and geometrically interconnected with the circumference.

In such a way that if we place it properly on the circumference or circle to be squared, it quickly produces a situation and alignment of two squares inscribed in this circumference, and whose anchor points to it define a superior square whose side is the square root of Pi, that is, the square sought for the squaring of the circle.

Curiosity: (drawing

I often proceed to squaring the circle, doubling the cube beforehand to find the cube root of 2.

For this, I use a compass with two fine needles, and a sheet of paper as a ruler, since this prevents the thickness of a ruler from preventing the perfect location of the compass needles at the appropriate points.

And it is precisely this work of doubling the cube that I like the most about the process, since in less than a minute the only measurement that is necessary to find the segment cube root of 2 is achieved.