Discovery of the true geometric π and Squaring the circle

26/₃₄	To avoid misunderstandings I will replace the color of the text in some sections below, to remind you that they describe alternative formulas. The wonderful π While waiting to discover how much the world scientific community shares this attitude, in my vision the new and increasingly enlightening perspective rises more to light: if we ponder for a while the hypothesis of recognizing π as a pivot or single parameter, such as the constant emerged from that side `VA`, here is a new driving paradigm, since it will have been its square, or the 4^th; power of a radical monad [0,88665] to give place, space and time to the golden number, whose powers above and below the one, alternate a concatenation of harmonic waves in perennial expansion/contraction, in a spiral pulsating both towards zero and the immense. Provided that the main radix does not reside precisely in the Φ, the gateway to our awareness, as a starting point and not a goal. An example of this is given by the spiral in the figure, which will probably meet more in nature than the one claimed, and which maintains the golden ratio in every corner of its path, intersecting any radius from its center in points that delimit contiguous segments always in Φ ratio. On p. 30 it was applied to the NASA photo of the Galaxy Silhouette. The popular golden spiral, instead, strives to represent a phi increase from a single quarter of a square to the next, entrusting and identifying, or confusing, a linear numerical increase with an expanding circular one; with the result of proposing a pseudo or false spiral. In truth, there are various ways of representing the iterative process, whose imitation of a spiral shows no other coherence than that, albeit substantial, of scaled squares wrapping around two fixed axes and containing right sectors of the circles just sampled. p.s. – Be that as it may, this golden spiral's matter, which left me completely unsatisfied, triggered a challenge to myself not so far from the π, such as to engage me in a further in-depth reserach in the following 2023, for which I promised a full resolution… and now it's done here! (April 8) more than i could think of.

26/₃₄

To avoid misunderstandings I will replace the color of the text in some sections below, to remind you that they describe alternative formulas.

The wonderful π