discovering the geometrical π
We all are children, especially scientistsNow, 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).
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 familyWell, 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.
The GestationNaturally 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,2√Φ, or the area L2 for4√Φ, 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.