Meter Unit of Measurement In order to square the circle with a ruler and a pair of compasses constructively as we know, the square should have the same area as the given circle. This theory of the squaring of the circle to be completed constructively with mathematic probative, the confirmation must first be precedent if 1 meter unit of measurement is correct. This is an essential point that has not been taken into account up to now. Because based on the radius of the circle (unit of measurement) the area is also defined by $\mathbf{ \pi }$.

Today mathematicians consider that circle cannot be squared due to the fact that number 3.14 is transcendental and irrational number. This consideration of mathematicians that circle cannot be squared due to the irrational number 3.14 …. is wrong.

(The squaring of circle already exists in nature. If the squaring of circle did not exist in nature then there would be no life – existence).

Any area of circle is squared even irrational numbers, as 3.14…. It simply remains to be confirmed below with evidence base of the mathematical formula: I.E. 2r-(2r/Φ)+r (I.E. Ioannis Eftimiadis) that 3.1415….. is not the real number $\pi$, because today’s 1 meter is bigger than 0.004846…. than the real meter unit of measurement. The formula I.E. 2r - (2r/Φ) + r has already proved the squaring of the circle and the real number 3.1415….. arises through the radius of the meter 1.004846… and not through the real radius of one meter unit of measurement.

In order to have a complete theory of the squaring of circle with mathematical evidence the objective from the formula I.E. 2r-(2r/Φ)+r should find the root of the area of the circle which is the side of a square. That is a2 = area of square, equal to the area of the given circle.

Proof We take the radius of the circle r = 1.004846…
Whose area is 3.14159… Subsequently we double the radius
2r = 2.009692…. We define the Golden Section with gold number Φ = 1.618…   $AB = 2r$
$A\Gamma = 2r \cdot \frac{1}{\varphi} = \frac{2r}{\varphi}$
$\Gamma B = AB - A\Gamma = 2r - \frac{2r}{\varphi}$
$\Gamma\Delta = \Gamma B + r = 2r - \frac{2r}{\varphi} + r$ The formula I.E. 2r-(2r/Φ)+r proves the square of the circle of rational and irrational numbers and in parallel today’s 1 meter unit of measurement is bigger by 0.004846…. Against the real 1 meter.

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