Squaring the Circle
Building Pattern for squaring circles

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

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

Email: ferman25@hotmail.com
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Drawing 1
Squaring the circle

Basic idea: Capture of the circumference as integer value

The essence of this method is the initial use of a hard and real circumference (and its interior circle) to get in real procedure the diameter of this circumference and circle to later on proceed to squaring the circle on the paper.
Later with these obtained data, we proceed to the construction of a Pattern for squaring successive circles easily.
For this work, we need firstly as tool a compass for capturing the diameter of the circumference.
Later on when we need the ruler for working and squaring on the paper, the ruler will be manufactured with the material of the circumference, which would have the longitude of 2.Pi.r of that circumference.

* Observation: Whatever the length of the ruler, there will always be or can be constructed a circumference of the same length.
This way and in good logic, we can not postulate that: With this ruler you can make all possible squarings, except the circle with the same perimeter than the ruler lenght.

In this work it is fallowed the requirements of:
-- The Compass can produce arcs and circumferences, also measure and transport segments.
-- The Ruler only can mark straight lines and unite points previously marked.

Working on

To squaring circles we go to squaring a first circle with a practical and real (hard) procedure and later on to build a pattern that allows us squaring successive circles using simply this pattern.
Why this procedure?
Because of we must to avoid the numeric value of the Pi number to be a transcendental number.
Later, and taking advantage of this procedure, we go to produce a pattern for being used in posterior squaring.
So, we proceed to make the practical construction of the quadrature of a practical circle, firstly step by step to explain it clearer; and later a more compact form of more easy construction.

Observation!: Like the Greeks considered, we understand that all tools and our own measurements are ideal and accurate.



And now a simpler and more compact way


Construction of a pattern

And now we proceed to build a pattern of Cartesian coordinates, using for that the anterior practical solution and marking inside the pattern the relative coordinates: (radii of circles (axis x)/sides of the squaring squares (axis y)).
Finally we mark in the pattern the straight line ( l ) that delimits the longitude of sides of squaring squares (f) in relation with the radius of the given circles.

This pattern is easy of using.
Firstly we take radius of the given circle with the compass.
Later on to mark this radius on the radii axis of the pattern.
Then, we mark the perpendicular from the end of this marked radius.
And finally we take the longitude of this perpendicular that is the side of the square to build.


Following it is shown drawings with easy representations of simple material that could be used
This method has been carried out with the below tools and materials with excellent and accuracy result.






Note: If once the circumference is cut to construct the ruler, it is demanded that this must to be completely rigid, then we can glue it under a wooden or steel plate, although this requirement seems to be little understood.

Some discussion about this topic

The below sentence has little consistence or sense, I think.
"Being Pi a not constructible number, it is also not constructible the root of Pi, and so, it is impossible the quadrature of the circle by rule and compass."

I think that assumption is not totally appropriate.
Pi is the ratio between the circumference and its diameter.
That is, a ratio, a division, an interrelation between two quantities, not a geometric figure.
Contrarily, the circumference is a geometry figure and also a constructible figure.
In the same sense, the sides of the square that give us equal area than the circumference is also a constructible parameter.
In the reality of facts, (for example a coin), the circumference and its diameter are integer values.
Another question is to find its ratio, but that question is expressly prohibited in obtaining the quadrature of the circle, since any metric notations is prohibited, only we can produce geometric figures.

* As you can see, this practical and real method is similar to many other theoretical ones of triangulation exposed through time, where the side of the square is obtained by the composition of semi-circumference with the circle's radius; but in our case when using a real and practical circumference to be squared its interior circle, I use the advantages that his method gives us.
That is, the possibility of taking the integer longitude of the circumference by means of the ruler, which has been manufactured from this.

An important or technic question to be taken in mind is that later on to be built the ruler this never it is used as flexible ruler, but as rigid ruler.

In the other hand, in not place is expressed the prohibition of using flexible ruler, mainly because all the rulers can be more or less flexible.
Nor is it forbidden or expressed that the circumference whose circle we are going to square has the same length than the ruler to use.
Nor is it acceptable the reasoning that this method is prohibited because in this case it is possible to square the circle.

I make this work because of I understand that who love mathematics should have the duty of trying squaring the circle.