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If the area of the circle /4 is0,19653784443935582151738964
and the square [side = 1] area /4/ 0,25 =
the constant ratio between the areas will be 0,78615137775742328606955857
that's to say Φ 0,61803398874989484820459
this is not reflected by the current value of π
where the area of the circle /4 is 0,19634954084936207740391521
with a circle / square ratio: 0,78539816339744830961566084
Conversely, applying the reverse process:
0,25 / 0,196537844439355821517389645
ie square/circle we obtain 1,27201964951406896425242247
that is obviously φ 1,61803398874989484820459
marvelous proof of the translation from Transcendent to Immanent
and of the inverse transduction, which are reflected so to say
below and above the 1
where the synthesis of the two processes or their direct multiplication
is equivalent to the UNITY and their sum to the 5, which introduces the becoming.
Ve­rum, sine Men­da­cio, cer­tum et ve­ris­si­mum:
Quod est In­fe­rius est si­cut quod est Su­pe­rius,
et quod est Su­pe­rius est si­cut quod e­st In­fe­rius,
ad per­pe­tran­da Mi­racula Rei Unius
«Smaragdina Hermetis Tabula» di Hermes Trismegistus
dal­la vers. lat. di H. Kunrath
What can finalize not only space, but also past and future
in fact is manifested in the formula:
5
±
1

2
Φ | φ =
for its univocal solution: Φ ×(Φ+1) =1, as φ ×(φ-1) =1
If the triangle is three [spirit], the square is four [matter] and the pen­ta­gon is five [transformation], we will have to think of the circle as One [Source of being] with the center zero, and thus attribute the two to the ex­tre­mities of the simple segment [duality, transit, polarity, com­par­i­son, connection].
We see then wonderfully interconnected the imprints of the first five forms: a symmetrical side of the triangle (the most significant  ), the square and the pentagon virtually contained and perfectly man­i­festable, with ruler and compass, in the perfect potentiality of the u­niqueness of the circle, from which all the others derive.
Subsequently and in support of such a survey, as well as of a probable forced imprecision, or transparent gap in the traditional definition of the π, some in­-depth reflections necessarily followed, and may suffice for as much as suf­fered, which I finally consider objective, inevitable and not eludable.