Few of these properties can be:

Logic development of the number Pi.

In the current development of the number Pi (algorithmic way) we don't use any parameter relative to the construction of the unit semi-circumference or circumference (r=1), but alone series of numbers, and to be algorithmic series the result is a transcendent solution.
Contrary, the squaring Pi is drawn and gotten with formulas of integration exclusively with parameters of construction of the circumference and Pi, and to be direct formulas, the squaring Pi has a real solution (irrational).

Formulas of integration .

In the below drawings are exposed the formulas of integration for getting the value of the Squaring Pi.

This method is based on the use of the Pythagoras theorem as for the number of powers that are applied to the rectilinear sides of the inscribed and circumscribed squares to the circumference (y) with integration of the diameter to this circumference (y'), making all those interrelation with the Squaring Pi (x) and the Squaring Pi elevated to the double powers than those of the sides (x'), with object of obtaining the final value of the Squaring P (when being this a curve)

This author thinks:
"The current algorithmic Pi is erroneous because of the circumference is treated, developed, extended and measures as a straight line (by mean of cut and paste in straight line pieces of the curved circumference) when the circumference is a curve line.
Reason: In the circumference line, all the pieces in what this circumference can be divided are nearer and closer among them than in straight line where all these pieces are completely extended, measuring logically more dimension than in curved line (circumference).
Then, if the relative distances among all the portions in the curved circumference are shorter than extended in straight line, also it must to be shorter the total length of the circumference than in the algorithmic straight line solution."

Thank you.
Fernando Mancebo.