The extended Pi number
Of ferman: Fernando Mancebo Rodriguez--- Personal page. ----Spanish pages
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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)
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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
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The stupid tale of the astronaut that did not age
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Reason for the Cosmos' creation
The extended Pi number
Squaring de circle with ruler and compass
The extended Pi is obtained by composition of a pair of internal segments to the circumference, of Pi/2 each, which, as seen in the drawing, are repositioned together forming a capital A, starting with the central segment placed on the diameter and center of the circumference.
The other two go from the upper point (O in the drawing) of the axis and of the circumference, passing united by the lateral ends of the central segment, and ending in their cut with the circumference (point S of the drawing).
Each of these segments represents an approximate value of Pi/2 (0.0009).
In any case, the important thing here is to consider that the extended Pi is a property and element of all the circumferences, and that it can be used for example, to square the circle within the measurement margins that the ruler and compass can do.
From the arithmetic point of view, squaring the circle is not possible because the number pi necessary is irrational, and even an exact division by 2 cannot be done to find the necessary side of the square.
However, and since what is required is to do it with a ruler and compass, in this case it is possible to do it since these devices cannot exceed three decimal digits of precision (aPi-> 0.0009).
Well, the example of squaring the circle that I expose is within these limits of precision of the ruler and compass does not exceed.
As we see in the drawings, this process is done in two steps.
Drawing 1.- Find the approximate segment of Pi,
Drawing 2.- Find the approximate segment on the side of the square.