Trisection of angles
Division with compass
Of ferman: Fernando Mancebo Rodriguez--- Personal page. ----Spanish pages
You can see many of my works, in the following pages:
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. ||| Atomic model ||| 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
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
The non-curvature of space by matter ||| The Master Clock
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)
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
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
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
Video Universal Consciousness||| Who is God ||| Web Universal consciousness
Creation: Highlights||| First steps in metaphysics ||| A personal experience
Reason for the Cosmos' creation
Trisection of angles
Division with compass
A first thought could be:
"With a good and precision compass we can dominate, section, divide, etc. segments, angles and circumferences".
As we see in the drawing, using the compass we can section, chop and mark angles, segments, rulers, etc.As an example we have the trisection of a given angle AB, where with an approximate opening of a third of an angle, we are putting the compass at one end, for example A, turning this with support at the "supposed" points c and d.
In very acute angles, it is better make the measurement on an arc farther from the vertex of the angle, in order to better use the compass.
In all these works to get the proper measurement we can make 2-4 attempts, and about 1 minute, and so, it is not an long measurement, because we quickly match points A and B and you can no longer improve.
To make a good measurement, you need a very sharp compass (the pencil or marker)
P.S: I think not only this method of sectioning angles and segments is easy, but it can be a good exercise for the use of compass in elementary students.
"Way to do the trisection quickly".
We open the compass an approximate third of the segment or angle to trisect.
Then we make the two movements of the compass for this measurement, and without separating the needle from the compass of the paper (second movement) and on the current opening, we add or substract a third of the rest that lack or surplus for the correct measurement.
And we measure again, until points A and B coincide with the compass.
The division of segments and angles with compass is very simple and general, and consists of making a single measurement but with several steps depending on the number of parts in which we want to divide the segment or angle.
In the case of wanting to draw inscribed polygons to the circumference with this method, the first thing we do is draw the starting point A on the circumference.
Then we open the compass with an approximate opening of a part of the division or side of the polygon that we are going to inscribe.
With this measure of the compass, fixed at the starting point A and lifting only one leg of the compass, we begin to rotate it, resting it on the circumference at points B, C, etc. to get back to point A.
If it doesn't match, we open or close the compass and do another test.
If after making the rotation, the compass makes the starting point A coincide with the ending point A, the measurement will be correct and we will point the points B, C ....., to draw the inscribed polygon.
A final consideration to expose would be the following:
If you can make an "ideal measurement" by opening a compass to take the length of a segment in a single measurement, you can also make "an ideal measurement" in a single measurement of two identical steps.
As a simple problem for this method we could put:
Given a segment A-B, divide it into three equal parts, only with the compass, without ruler.
As in other cases, to get the proper measurement we can make 2-4 attempts, and take less than 2 minutes.
(Here we see the last attempt with a correct result where we have made A coincide with B, and where the measurement ends)
The division of segments and angles with a compass can be considered similar to the arithmetic division of number:
if, Ac = AB/n, then Ac x n = AB
Where AB and Ac are segments or angles, and n is a natural number.
Thanks you friends.