The comparison of the two modes makes it clear that the diameter is a segment along which a point can slide from A to B and vice versa, approaching or moving away from C in an amorphous way, where the arc of circumference that starts from B can reach A only along a trajectory that always keeps it at the same distance from center C; then from A back to B while maintaining the same direction of rotation in the underlying phase as such introduces the concept of cyclicity, with it that of the time as well as of the sound and the undulatory process, not to say of the gravitational principle; but above all it circumscribes a space, whatever the angle of the arc, something that no straight line can do.
It is interesting to meditate on the contrast of the outward / return processes at the dimension that I have termed amorphous, where a point on the segment AB can return from B to A only by reversing the direction, ie the sign ± of the vector, giving rise to a condition of dichotomy or dualism: forward-backward (this is the case for changes in direction at the vertex-sides of a square or other polygon); while on the circumference there is continuity and completion, without contrast or interruption, only π.If we then wanted to plot a quarter of π equivalent to
The same is true for the area of the circle, entrusted to the formula
These primitive reflections are intended to introduce a deeper motivation as to why it was difficult for me to understand the acclaimed inapplicability of the use of straightedge and compass precisely to pi, despite the rivers of mathematical literature that claim nothing but that; but instinctively I was turning to the one in essence, whose harmonic and intrinsic function cannot be distorted, something that I would have tried to ascertain in a purely logical and analogical way.The next step will be to present something special, which geometry has always reserved for us, but which was never made known until 2003, the year in which I published an essay that started, among other things, my first analysis of the profile of section of the Great Pyramid of Giza; a first stage already with an unprecedented result, despite the myriad of writings and calculations inherent to that theme everywhere and to superficial applications of the
An elaborate that I must cite because it turned out in many ways almost a preliminary compendium of my research, to the point of leading me to the current findings.
The current development will not exhibit complex mathematical calculations or formulas, of which it does not need, but only numbers resulting from the notations, being properly dedicated to those who intend to make use, even mentally, only of straightedge and compass.