by Ioannis Efthimiadis

The problem that was given by the ancient mathematician (ARCHIMEDES)
concerning the **squaring of the circle by using ruler and diabetes**
challenged me to take the time with it, just as many people did in the past.

This known and still (**unsolved**) problem it’s true that it has bothered for
more 2000 years many mathematicians and not only them, and it will remain
unsolved for the years to come.

This happens many times; a difficult maths problem ends up in an easy
solution and vice versa. This actually means that there is always a solution,
unless the clues of a problem are given incorrectly, just like this particular
problem (our problem). Let’s see the basic **mistake**, why the circle be
squared from its real dimension.

We know that if take the diameter of a circle 1m. its length **is said** to be
(3,1415…) m. a transcendental number (infinite). This is **right**, that
(3,1415…) is a transcendental and irrational number, and it was proven by
Ferdinand Von Lindermann 1882 (a) and Johann Heinrich Lambert
1761 (b).

For this reason and only, because of this (particular) irrational number
( 3,1415…) which was given **wrong**, the circle cannot be squared. It is
logical! Because it is not the **real** π. number, the QUOTIENT.
Since there is no theory or a formula that can prove or check the π (3,1415)
the length of the periphery of a circle to its diameter that was given, then
there can be a doubt if it is ( correct ).

__Theorem and Proof I.E. ( Ioannis Efthimiadis )__

In order to square the circle we have to know its two basic factors, the **real**
number π and its radius. The first meaning of squaring the circle means
that I check up the number π, in connection with its radius to the basis of
the square. The second meaning is that they must have the same area.
Therefore, up to today, they haven’t managed to square the circle and to
prove number ( 3,1415…).

The ( 3,1415…) is a number approximate to **the real number π**. The
proven **number π**, with the formula ** I.E. 2r-(2r/Φ)+r** is an Sacred
number:

__π I.E. 3,111...__
__Confirmation of π I.E. 3,111… with the formula I.E. 2r-(2r/Φ)+r__

We take the radius of a circle 1m,

Which covers an area of __π I.E. 3,111…__

Square meters ( shape 1 ).

**and we shall prove the**

__I.E. 2r-(2r /Φ)+r__real number

**in the**

__π I.E. 3,111…__following shape (2), (3) and (4).

1m and we double it

**2r = 2m**

(shape 2).

2 r = 2m with the golden number Φ

(shape 3).

The formula **I.E. 2r-(2r/Φ)+r** confirms the **π I.E. 3,111…**

in relation with the radius of the circle, to the basis of the square,

so that the square has the same area with the circle.