discovering the geometrical π

We all are children, especially scientists

Now, speaking of gen­e­sis, given our context we will first have to es­tab­lish the official date of 'birth' of the π. In the absence of [ge­o­met­ri­cal­] as­cer­tained origins of pi greek, we consider it for­mal­ly en­shrined by the now tra­di­tion­al 'pi day' on March 14th, the birthday declared at the San Francisco Ex­plor­a­torium science Museum, which refers to the first figures 3.14 (leav­ing out other lo­ca­tions resulting from a­dapted cal­cu­la­tions, 314th day etc.).

Following the same in­spi­ra­tion, we will also a­dopt the hour, nec­es­sary for an astral chart, using the figures after the first three, use­ful where con­vert­i­ble in terms of hours and min­utes.
In the case of 3.14159 they could correspond to 15:09 or 01:59; however, adjusting the time to 04:06 from 3,144605511 (which we will soon dis­cov­er the reason for), im­me­di­ate­ly offers at least one irreplaceable reference, math­e­mat­i­cal­ly unique on 21,600 cases.
Here, then, is the 'pi' horoscope according to this arrangement.

The ‘Anamnesis’

Two things stand out immediately, both of which refer to Pluto.
Pluto is the profound, the unconscious, the invisible Power; its orbit en­vel­ops the entire solar system; its angular influence often appeared crucial in the heaviest seismic events.
In this theme it dominates the midheaven, in one of the seven regal de­grees of the zodiac! and unique among the planets, its initial letter is P, com­po­site inPL in sci­en­tif­ic symbolism (after astronomer Percival Lowell dis­covered it).

The second, clearly legible, is that the axis of opposition that it forms with Venus – both in their zodiacal domicile – not only divides the e­clip­tic in two, but separates all the other planets on the same side, leaving the other half of the sky empty: a com­plete­ly one­-sided scenario, which looks to focus on the priority of the Moon within one degree from the As­cend­ant on the side of the ego sec­tor, wide Field I with Mercury in the cen­ter, (com­mu­ni­ca­tions, study, in­tel­lect therefore also ra­tion­al­i­ty and cal­cu­la­tion).
It is worth adding that in my studies the Plu­to­-Ve­nus axis has a specific val­ue, described on site; but the topic of the article is quite dif­fer­ent and I won't dwell more than necessary.

Those who do not dislike symbolism, will notice that this precise moment has brought together in the celestial map two figures whose relevance could not be greater: the sun [Sun] , a circle animated by its center, is in close con­junc­tion with the axis of the Lunar Nodes, representing the two points, North and South called “head and tail of the Dragon”, the in­ter­sec­tions of the lunar orbit around the Earth with the ecliptic path, focuses on the adaptation to the environment and the balance of choices and, cycle after cycle, retraces the solar circumference.
Its representation therefore rests and joins the two nodes, with a stroke that e­vokes a rounded π; but that's not all: the so-called Part-of-Fortune (technically the Sun-Moon equidistance from the Ascendant, an­oth­er sen­si­tive point that has proved to be of constant importance in seismic events) strength­ens the com­bi­na­tion be­tween the two in very close conjunction with a circle or wheel symbol quadripartite.
They come together in a perfect trine to the Midheaven.
The combined strength of the three points, however, is found in a decisive dys­to­nia with Venus which, in addition to governing the sector that hosts them, is the 2nd guard of the half of the circle occupied.

On the other hand, Jupiter on the cusp of Taurus and master of Pisces, the sign oc­cupied by the triptych just described in Field II, with a beautiful trine to Uranus-Saturn in turn in close conjunction, is however doubly guar­an­tor of the most jovial cel­e­bra­tions, associated with science though, rigor (Sat.) and technology (Ura.).

Lastly, the most sensational detail, so much so as to put myself in a certain em­bar­rass­ment, since it might seem done on purpose: the theme, although erected in the most total abstraction, respects symbolic canons even if the date and time are derived from a constant which has neither format nor temporal purposes.
Well, the application of the figures 3.1446 that sooner or later we would like to re­place to 3.1415, has stopped the second hand, that is the As­cend­ant for each astral chart, with undoubted precision at 3°14'+, a cal­cu­la­tion re­sult that couldn't be intended or foreseeable, which anyone can verify; this is what is obtained by applying said time both to the generic co­or­di­nates of San Francisco and to those of the Ex­plor­a­torium Science Museum itself; and the Ascendant, as we know, characterizes the individual or event in a more detailed and direct way than the Sun itself.

This is not what I intended to go into, but I must say that there is more than I ex­pect­ed. For all intents and purposes and with or without pi, this theme remains valid as a full-blown celestial chart of a historical event.

Having erected the horoscopic theme, however, does not provide indications on gen­i­ture, the most important side for our investigation. Will this special infant have a fa­ther and a mother? and how could it ever be?

The family

Well, the answer, surprising as it may be, it is positive at all: as a first homage to the family name, the letter P is re­garded.

π in fact boasts a lineage of absolute respect: Phi [Φ] the father, phi [φ] the mother; a truth that has remained hidden for millennia within the Great Gold­en Triangle, dis­covered in ex­am­in­ing the section profile of the great pyr­a­mid of Giza, described for the first time in 2003 in my treatise on the '5 Tibetan Rites'.

So let's see what authorizes such an impromptu assertion.
Since the mentioned virtues of this entity refer to the golden section, and since our research is oriented to the circle to identify the golden principle that sustains and pervades it, we will start from a unitary dimension circle, ie of diameter = 1.
The first step to focus the functionalities of the golden section through this circle will be to apply it in its ideal form, that is to say by drawing a cir­cum­fer­ence that is nat­u­ral­ly con­cen­tric with it, with a diameter of Φ.
The writer knows that might suffice, but in order not to deprive the reader of a su­perb in­te­gral path, he will go to a third circumference, always con­cen­tric, with a di­am­e­ter Φ² and then one more with diamete Φ³.

Everything said, or what will follow, can be done with ruler and compass, although I will not try to prove it here (it is detailed both in the first part of this site and in the essay presented at the end).

This 3rd power, say of ideal reassertion as in a deed of concentration, au­thor­izes the next step, which consists in fixing the base, or "Φ-father" [contraction – yôn – energy] simply by simply drawing a rope AB of the larger circle, which is tangent to the small­er circle.
It is now a question of constructing the corresponding “φ-mother” [ex­pan­sion – yin – mass]; but since its length will be considerably greater than the diameter = 1, to attain everything strictly inscribed in the larger circle it will have to be composed in a dou­ble rope; but it is quickly solved.

In compliance with the biblical pro­ce­dure adopted to extract Eve from one of Adam's ribs, we will thence use half of the string AB, to con­struct on the base mB the square from which to obtain by classic meth­od its π thanks to the simple arc heq, where h is obviously the mid­point of mB.
Center on B, just project the dis­tance qB, which is mB × 1.618, a­long an arc that will in­ter­sect the larg­er cir­cle ex­act­ly in V, up­per ex­treme of the ver­ti­cal di­am­e­ter, thus de­fin­ing with VB the half of the φ-mo­ther from us looked for.
If it is even surprising that VB is tangent to the 2nd circle with diameter Φ, well, that's only half of what we're going to check; since, completing with the symmetrical side VA we will have configured the “Great Golden Tri­an­gle”, whose base will be in relation Φ with the sum of the two sides.
In a word, all that triangle whose perimeter is Φ-father + φ-mother = 5, it is itself golden section at the pure state!

The Gestation

Naturally it is the mother's task: since as we will see, its length is equal to half the circumference (this is not the seat of ac­a­dem­ic dem­on­stra­tions, but only of more or less transversal utterances) we pro­ceed to complete it, like a kind of mo­ther's womb, tracing the specular re­flec­tion FDE, ie by duplicating the two sides AV and VB in vertical symmetry FD and ED, with the vertex D at the opposite end of the di­am­e­ter, the sum of the four will be the linear measure of the cir­cum­fer­ence, but above all and as if by magic, their points of intersection on the line of the horizontal diameter, will define a seg­ment, the newborn, that is the true π, of proven ge­ne­al­o­gy, like a jewel in its cas­ket: 0.786151377757423286 even if by sec­u­lar con­ven­tion it will be conceived mul­ti­plied by four (= 3.144605511029693144).
Truly, all this stage set would not be necessary, if not to emphasize a story that, though it may make you smile, cannot fail to force us to reflect.
In fact, one side of the triangle just built is not only in relation φ with the half of the base, but has the same length, of the aforementioned π, and are none other than the square root of the absolute Φ diameter of the 2nd circle: 0.78615…; which equates it to ¼ of the most popular value – a figure devoid of genetic roots and coated with ap­prox­i­ma­tions – with a positive pro­por­tion­al increase and realistically justified of 1.000959 ...

At this point I would suggest a great deal of caution to release the in­stinc­tive reaction for which it would be this value to border the most official with a more or less ac­cept­a­ble deviation.

Demonstrate the indemonstrable? the constant to which VA and each side lead back, defines in a linear way with incisive certainty a quarter of the greater circle. In addition to having reproduced the total length of the circumference in a rectilinear inside way, their intersections in the points pg will define a segment of equal length to each of the four sides, again the side of a square whose perimeter equals the cir­cum­fer­ence.
Which, if that is not enough, is also the intermediary between the Unity and the Φ, since its value of Φ is 0.78615137775742328606955857332… from which 1 ÷ 0.786 = 0.786 ÷ 0.618 = 1.272019649514068964252422482, that raised to the square is = 1.618…

It therefore remains to be established which of the two is closest to the other, if the π with a genealogy or that … orphan.

To tell the truth, the latter has far too many parents; the other one can not claim that the Cosmic Intelligence.
Do you find all that so bizarre? Father_activity|Mother_stability – Fa­ther­_e­lec­tric­i­ty|Mo­ther­_mag­net­ism in short, masculine and feminine are the two universal prin­ci­ples and found­ing poles of the Reality: out of their combination does a whole child take shape; and the π it is an architrave that rests on two pillars, sub­li­mat­ing their balance in the vital Intent universal, and evoking more than one sa­cred sym­bol of tradition.

Can we afford to ignore all this, in support and approval of a π discretized?


That's it, the scientific community has all the time it takes to reach a def­i­nite and de­fin­i­tive conclusion.
What in the meantime should add up specific evidence is that the artifices up to the limits of refinement for a π prefabricated, articulated by in­di­rect operations discussed at length and built on experimental bases in­de­pend­ent of the nature of the circle, al­though re­fined to the bitter end, they could not miss to con­tem­plate a margin, ob­vi­ous­ly min­i­mal, of error, both for the kind of approach, concentrated on a single circle, and/or for the ac­cu­ra­cy of the ac­tu­al calculations, inevitably limited compared to the circular entity.
After all, the most valuable gift that can be given to the meaning of pi day is to mo­ti­vate it with a renewed enthusiasm (even if this may upset those who have already memorized a rosary of decimals, to be exhibited in com­pe­ti­tions…).

As for the Quadrature of the Circle, both 'geometric' and mathematical, it finds tout court its unexpected and one-to-one solution in a mentally very simple, but in some way innovative passage: it is sufficient to circumscribe a square to a circle of di­am­e­ter L, and then multiply both geometrically and mathematically: the perimeter L×4 by the aforementioned constant,2Φ, or the area L2 for4Φ, ie semantically figuring, 4 times L for π, and the square of L for the square root of π.

The booklet “2x2 = 3.14” illustrates everything I have exposed, and proposes the rea­son for the possible tolerance of 3‰ in the presumed exact calculation methods in lack of a known geometric π.