An incredible theorem for a unique and effective equation to determine the universal constant Pi π definite and definitive After millennia of attempts to calculate the circle with all sorts of simulations, until recognizing an identity to π, and yet with results often different and disputable, all that was missing was to be able to ‘bring it out into the open’ to identify it with certainty and without any approximations. This task was accomplished by the "Pi-draw­er", a ge­o­met­ric de­vice de­signed to lit­er­al­ly ex­tract from the cir­cle and per­form the ex­act cal­cu­la­tion of the re­al Pi con­stant, by means of a 4th degree pol­y­no­mi­al e­qua­tion, with ra­tion­al co­ef­fi­cients and a single variable. The theorem was ultimately matured in four years from a first introductory publication "2x2=3.14" (2021) about the squaring of the circle, followed by several articles and evidences to point out the actual π against reiterated adaptations, but unable to demonstrate it. The alleged impossibility of achieving the Squaring of the Circle has thus been overturned in the same context. Some further details and additional descriptions are implemented at the Repository URL.

As to the theorem, both the basic one and here its alternative way always de­fin­ing the π as unknown - but instead of bringing the circle towards a square, it starts from the square to obtain a circle of equal perimeter - are e­ven­tu­al­ly re­placed by the closest analysis that setting the ¼π as a constant, re­leases the implicit proof into the Pi-drawer in an immediate and accessible way. From the effect of that second perspective, new postulates emerge with im­pli­ca­tions, regarding the transition from the circle, whose monad is the root of the golden section, to the golden spiral of any density or amplitude.Once discovered how the golden ratio pervades the nature of the circle, as its soul, here's a first look at how it amplifies its manifestations through the true Golden Spiral, which punctuates the squaring the circle itself with every ⅛ rotation. Far from being a half circle with radius 1, [¼]π, which I like to call 'Platinum', is the pivot of the world.

This amazing solution was attained through an inverse geometric process, as it allowed to exactly extrapolate the natural π from the circle itself, converting it into a manageable rectilinear segment. As a must, the introduction to the «Cosmogony of the Golden Section», which is closely related to π, being fundamental for the semantic and epistemological trait. NB - Its release date is prior to the demonstration of the actual "Pi-drawer". This enhanced 2nd edition updates and replaces the previous one, not in terms of con­tent, which remains unchanged, but to offer additional considerations that aid understanding, after the laborious effort of structuring the initial conception.For some minor typographical corrections of the first edition, it is integrated here afresh; to be completed by significant ac­ces­so­ry notions.