Squaring the circle with two squares
Of ferman: Fernando Mancebo Rodriguez--- Personal page. ----Spanish pages

Hi friends,
I tell you a little about my rare experience.
I have been chasing, surrounding and harassing for a valid Pi segment for some time, and when I think I have discovered it in some unexpected place, it appears and responds: "I'm sorry, but in the form of a straight line or segment I am often nicknamed as a Phi number"
So I always end up convinced that the Pi number is about a thousandth longer in straight line than the curved line (keep the secret, please.)
Be that as it may, here I put a square of the circle with respect to the Phi number, because I see that it is very simple and interesting in its construction.
Thanks friends.

As we can see in the following drawing, there are multiple pairs of twin or repeated segments, relative to the number Pi, that occur within the circumference. But when measuring them and trying to relate them to the segments relative to the radius or diameter, we can see that increasing in dimensional difference that I have previously explained, with which we could already begin to think that the circumference certainly acquires a little more dimension when it is extended in a straight line.

Summarizing:

In principle, the circle cannot be squaring with respect to the number Pi, but it can be squaring with respect to the number Phi.
And to my understanding, the number Pi is the geometric derivation inside the circumference of the number Pi, which acquires an increase when it is derived or transformed into a rectilinear segment (of the order of 0.0001 x 1-- 0.01%).

Squaring the circle regarding to Phi  The simplest practical way

For this practical development, I first use two squares as tools, and then the compass to make the square root of Pi/2.
Of the two squares, one will be semi-fixed and will always be aligned and join to the points O and C (centre of the circumference), as shown in the drawing.
Therefore, this will be the reference square, and will only have the ability to rotate (without leaving points O and C) to take the necessary positions to achieve the coincidence of points (p) and (q), and thus form the parameter (1/phi).
The other square will be movable as shown in the drawing, and its mission will be to mark the points (p) and (q), and later check if they are aligned perpendicularly with the diameter of the circumference.
With the proper movement of the two squares (as shown in the drawing) we will achieve the perpendicular coincidence of the points (p) and (q).
Once this coincidence is achieved and parameter (1/phi) is obtained, we mark the segment Pi/2.
Then with a square and compass, we proceed to obtain the segment (b) by mean of the square root of Pi/2.
This segment (b) is the semi-diagonal of the final square we were looking for. * The squaring to the phi number does not theoretically correspond completely to the squaring to the Pi number, but in practice and on paper and drawing, the difference cannot be seen neither with our vision capacity nor with the precision of our tools.

You can see many of my works, in the following pages:

Email: ferman25@hotmail.com
Email: ferman30@yahoo.es