This page documents at least one proof unknown to the global mathematical tradition, precisely because it hinges on the authentic π (download it in PDF).

February 2024 -A proof that cannot be refused

Concentrating on the character of the circle through the radius, which is its only key, implicitly leads to focusing on the quarter of the circle, or quad­rant, as if this could identify the square as the most practical ref­er­ence matrix from a rational point of view, to the function proper to π.

I propose it a­gain, as an echo of my es­say, in a sym­bol­ic in­tro­duc­to­ry scheme, which seems use­ful to me to re­pres­ent the re­la­tion­ship be­tween square, nat­u­ral π and cir­cle, de­lib­er­ate­ly con­sid­er­ing the π as re­lat­ing to only one quar­ter at a time, i.e. 3,14…×¼.
Based on a radius R we can construct both a 90° arc and a square with side R, which circumscribes it.

It is easy to observe how the sum of the two sides, upper and right of the square for greater visual relevance, are curved × π over the arc ¼ of cir­cle. Thus the formula with π quadruple describes the circumference.
The same canon concerns the area, which reduces the square of the side­~ra­di­us to the area circumscribed by the arc and double radius.
It is a mental exercise, but useful for strengthening a concept of rec­i­proc­i­ty, which I will try to delve into in an exclusive way.
Every medal has its own reverse
An exceptional medal, with a square face and a round back!

If you can accept for a moment the value of π natural [3.1446055…] proposed by my research, you will find that not only a square
with perimeter: 3,14460055110296931442782342932803
whose side is:0,7861513777574232860695585
has area Φ:0,6180339887498948482045868

but also that
The marriage of true π and Φ in the square~circle ratio

a circle withequal perimeter, i.e.
 circumference: 3,1446055110296931442782342932803
 thence radius:0,5
 has area Φ:0,7861513777574232860695585

The legend of this comparison is simple and clear: the perimeter of a square with area Φ is equivalent to π which I support. If this is the true π, a circle with a circumference equal to said perimeter has area Φ, being its ra­dius = 0.5, which when raised2 and multiplied, divides π~cir­cum­fer­ence into four parts [0.78615…], i.e. the sides and the square root of the square's area.
The area is obviously greater, as it is known that the circle is the figure that encloses the largest space of any other with the same perimeter; in this case the ratio between the two areas, is exactly φ (1,618) !

Of course, a square with the same area as the circle will have the side = 4Φ

I purposely use descriptive language, to highlight the semantic side of the for­mu­la­tion to the mind. Can't we perhaps read the prerequisites for an effective symbiosis or stringent square-circle connection?

Focusing on the term "square root", one can easily deduce its double mean­ing, referring it to the figure of the square, the only emblematic one for this type of operation: 'root' indicates the side, 'square' indicates the motion im­plic­it in the relation between the side of the square and its surface, which multiplies the side by itself; but as in nature, it also in­di­cates its e­mer­gence.
From what we are observing in the two figures, two faces of a shared truth on the crest of the golden ratio, we could argue the extraordinary statement for which:

the circle is the root of a square having the same perimeter π

or that a circle with perimeter π, squared, has the area of a square with perimeter π ! It is a cardinal factor of interaction of two dimensions that are not only mathematical: mass from energy, but perhaps also phys­i­cal from met­a­phys­ical.

A circle with the same area Φ as the square has radius = 0.4433258966 and circumference = 2.788170071589; but in particular, the area of the cir­cle with perimeter π i.e 0.7861513777574232860695585 divided by the ra­di­us of the circle with area Φ: 0.44332588966 is = π.

How can one explain, or classify the fact that π discovered and introduced as such by my research generates all these combinations of enormous im­pli­ca­tion – and who knows which and how many others –, dominant of cal­cu­la­tions and conversions, where a prefabricated π does not give rise to any supporting formulation?
Notwithstanding that neither of the two is demonstrable, one being a very close hypothesis of what the other should be, none of the above takes place if it is left to π the conventional value 3,1415,
whose results above would be
circumference: 3,1415926535897932384626433832795
with a radius:0,50047951115439126298184912117078
r20,2504797410853384486234931621638
× π =  0,78690531446677277387799027424776
thence area2:   0,61921997393605054860809869132551
Given this discrepancy (could it really just be a chance?), we can and sooner or later will have to reconsider:
  • If the circle of circumference (and π) 3.14460..., which is perfectly re­flected in the square, is worth more, what the current advance of the π should have at least suggested.
  • or you opt for a circle with circumference 3.1415… which does not cor­re­spond to the square, ignoring tout court the wonder exposed here?
    give up such a melody in the name of a makeshift construct?
Although so much supported, we cannot overlook that current π is the result of an artifice pushed to the imaginary limit, to the so-called 'infinity' which however we cannot reach, and which does not arise from any law implicit in essential geometry – as such, indeed, a certificate of pragmatic impotence.

You can push the number of sides of a polygon to the extreme, but you can also force the radius of the simulated circle to infinity, and the gap becomes larger to the eye.

Again as I see it, the π current after much pilgrimage in the most con­vo­lut­ed and illusory meanders, he has reached the walls of the longed-for goal, but he lacks the key to access, since the key is precisely the π.
Yet it is not a demerit, if we recognize that π represents a mathematically indefinable goal, if not an insurmountable bulwark for rational intelligence; and not for reasons of transcendence, since even the Φ it is, and yet there is nothing easier to demonstrate and reproduce.
Returning then to the topic of ruler and compass, if we associate algebra with the ruler, the compass is undoubtedly the π, and no ruler can replace it.

At the current state of progress, it deals with a gap of only 3.01 thou­sandths (0.1965 for the π by ¾),, as yet insurmountable in light of the traditional po­si­tions.
One may wonder whether there are too many to be acceptable, or whether there are too few to worry about.

Try to visualize a beautiful and simple soap bubble, splendid, de­fense­less and extremely rare expression of congenital equilibrium, which hov­ers in the air reflecting the environment and the colors of light on its brilliant liquid veil, kept in balance by the gravitational or elastic laws manifested by π native.
Now suppose for just a moment that you can replace it with the cur­rent π precalculated; can't you imagine what would happen?
The bubble would explode into a myriad of micro-droplets, such as to sug­gest more than the 131k side-segments of the last simulation polygon inscribed in the circle.
Is it not likely that the molecular or even inter-atomic dynamic con­ti­nu­i­ty of the surface can never be supported by the many flat faces of the hypothetical polyhedron, whose only vertices would come into contact with it?
There is one last leap towards the imponderable; not scientific, in the common sense, but for my analysis it is, rather than remaining stuck at the current limit.
In reality, the only way to conceive the golden lineage of π is the courage to take flight on the wings of pure intuition, which allows us to jump over the separation of two sides that no mathematical bridge will ever be able to truly and de­fin­i­tive­ly unite, for the reasons already explained on page 15-16 of my essay, from which it can be deduced that any attempt to define π would require the π itself so as to be demonstrated, not an assumption of the same.

The academic world can only make use of indirect verifications, such as the pro­di­gious rendering just represented, which is of in­dis­pen­sa­ble and ir­re­place­a­ble evidence; and even before that, that of the Divine Golden Triangle, first revealed in 2002 with my treatise «The Secret of the 5 Tibetan Rites»" in its most evident properties, removed by a Wikipedia expert because it is inadequate, but only 12 years later understood and illustrated by me in its deepest sense, elevated and indisputable.\
However, it was not such a damage to affect 20 centuries of knowledge for just 11 years of delay...
In spite of the actor, in fact, such an exhibition of 'learned ignorance' could only exalt the concept of self-evidence, ie of those special first fruits as seals of the creative Truth, which Nature bestows on those who know how to read it, and who led me to the most decisive goal.
A bit like Isaac Newton's apple, where nothing could be seen.
Inscribed in the same circle of radius 0.5, it in fact bears at the apex of the shape, both Φ and φ, and the right π which it enunciates in its sides.

It may be objected that all this does not involve any demonstration, but how many other randomities do we know that can complement or dilute these, reducing their un­a­void­a­ble im­pact?

These free considerations remind me of that very special message "The Origami of Power", which a luminous Entity at my side had delivered orally to me by someone who didn't even know the meaning or the reference.
A reference that becomes increasingly clear today, even for me
.
So much so that at this point I was forced to reveal one last fold of this astonishing origami, which I had not mentioned in my last proposition on the divine character of the wonderful triangle: and it is that its area is in φ2 ratio to that of the circle in which it is inscribed; but this also, only if you ap­ply the correct π.
Immediately note the link between this and the two figures already tested: the triangle [3] is inscribed in the circle [1] of area Φ, and has 2 sides equal to those of the square [4] of area Φ while its base is Φ of the sides.
It looks like a 3.14 cabalistic game.
In the circle with diameter = 1 it is Φ/φ2 = 0.300… (with minimal ap­prox­i­ma­tion-, it's like saying area of the circle /φ2, where at my first ap­proach the four pri­ma­ry symbols of square root, square exponent, are ar­tic­u­lat­ed on the two com­ple­men­ta­ry values of the golden section, in addition to my ge­o­met­ric description highlighted in the link above, to the 8 No­vem­ber 2023.
 Our Third Treasure of Geometry
The calculation procedures are multiple and easily deduced from the figure:
Da AC² - BC² via Pitagora we obtain AB, half of the base of the triangle.
If the radius of the larger circle AC is 0.5,
that of the smaller circle with diameter Φ3, or in any case 0.5 × Φ3,
is = 0,11803398874989484820458683436564
and so 0.25 - 0,01393202250021030359082633126872 is
AB = 0,48586827175664567818286387589454, equivalent to golden
section AS of the side AV which × Φ (height of the triangle), gives its area
i.e. = 0,30028310600077760788669470994843.
A truly unmissable 3, cut to the thousandth, suggestive and emblematic giv­en the relevance to a circle with a diameter of 1; but it is not the cal­cu­la­tion on the triangle alone that is destined to make headlines in school books.
In fact, the remaining decimals are crumbs justified by the exact calculation of the golden section, which confirms an identical result, also by Φ×Φ2, where Φ is the area of the circle 0.78615, in its precise and ex­clu­sive golden ratio ÷2.61834 or ×0.61834² with that of the in­fi­nite­ly rep­re­sent­a­tive triangle. Well:
the ratio circle÷square is φ : 0,78615 / 0,61804 = 1,2720,
the ratio circle÷triangle is  φ2 : 0,78615 / 0,30028 = 2,6180
the ratio AB ÷ BV of triangle is  Φ : = 0,78615, ¼π, ¼ of circle
This is a magnificent proof of the mathematical superiority of π 3.14460.

THE AREA OF THE TRIANGLE IS IN DIVINE PROPORTION Φ2 WITH THE AREA OF THE CIRCLE THAT CONTAINS IT WITH A PERIMETER OF 4 TIMES ITS SIDE; AND IS E­QUIV­A­LENT TO THAT OF THE CIRCLE WITH DIAMETER Φ TANGENT TO ITS TWO SIDES.

Could we deny, if anything, such a complete correspondence between this triangle, the third treasure of geometry, and the circle with area defined from the π par excellence, the only one which can determine their golden pro­por­tion?

Given that with the conventional π of 3.1415, the recalculated area of the tri­an­gle would only reach 0.2988, and above all the golden ratio with the circle would collapse, if we cannot afford to classify this latest proof as an irrelevant coincidence, we will have to admit it and annex it to the path ad­vanced to date, as a completion of explosive evidence.
It is a test bench that would make it very difficult to support the thesis of a π precarious, whereas the π here declared 'native' abounds in glaring per­fec­tion.
It will probably only be a matter of time, as often in the history of human cul­ture, to bow before such a geometric miracle and take note of a mag­nif­i­cence that has remained hidden to speculative thought, but has finally re­vealed itself to our eyes leaving no room for contestation.

Alessi Antonio Nothing could have been condensed more concisely, completely and ex­clu­sive­ly than in this cosmic symbol.

work in progress
Past or future, the potency of 4 is in the π × every season
From North to South and from East to West, even before the four El­e­ments: fire, earth, air, water of the varied Greek philosophy – it is e­nough to mention Empedocles' the four roots (rhizai) which will lead all things back to the sphere original: the ‘Sphairos’ – the same four arithmetic op­er­a­tions, integrated by square and square root, in material and symbolic know­ledge, from the four seasons to the phases of the moon, from the wave phases to temperaments in medicine and psychology, this and more contributes to modalizing reality into 4 distinct and congruent realms, con­trast­ing and complementary, com­bined by continuity and completeness.

We know well that the definition of π it arose from the need to calculate the circle seen in its entirety; but if this does not prevent us from discovering that a fourth of it is equivalent not only to one of the aforementioned com­ponents of the unit, but also to a constant that regulates

4. The Effect of Direction of Particles
There exist some differences between particles receding and those approaching each other. At extremely high relativistic speeds, objects approaching each other have a repelling effect. When objects approaching each other are at 0,78615 c, their inertia equals to their gravitational affect. For particles approaching each other at still faster speeds, the gravitational effect will have a negative repelling gravitational effect.
it is clear that with a constant value of 0.78539, ¼ of π too approximate even from the 3rd decimal, said gravitational and attraction-repulsion bal­ance would fail.
On the other hand, even if the authors of the cited research did not deal with it, nor could they probably have imagined it, it seems legitimate to fo­cus on the value of π effective with this elementary module as the most promising, which will not fail to give greater eloquence to the prospect that derives from it and unites the three cases explored here.

Table for our three models, with π = 0,78615…

SQUARECIRCLETRIANGLE
base | radiusπ 0.5 1- π12
perimeter4π4π2π / π2
areaπ2ππ5

It can thus be seen how the true π carries out its balancing function not only in physics with the motion of particles and so on, but in the same way in the world of numbers, as a matrix of the golden section in the dual man­i­fes­ta­tion of increase and decrease, in a spatial and perhaps temporal sense.

In any case – recognized the Π fundamental – the Unit of Measure to refer to turns out to be a single Source, the key that encloses and originates both our and Φ and φ: it is the figure
0.78615137775742328606955858584296 for which 5 decimals seem to be enough, if only because the following two di­min­ish and justify the ap­prox­i­ma­tion, in a research in Physics at its first steps.
As I proposed at the beginning, approaching the circle according to the rhythm of 4 quadrants denotes that balance is formed from contraposition.
By the way 3,14460 / 4 is exactly = 0.78615, which when squared re­spects the first 5 decimals of 0.61803, two more than those commonly applied.

Pi day Horoscope

Pi Day fans might be happy to realize that it's about tasting slice after slice of the pie, and not all the cake in one go ;o)

By the way, I cannot help but notice how curious it is that on the date I am writ­ing, the planetary and astrological con­fig­u­ra­tion is so similar to that of the day on which the Pi Day was born, as for the rare unilateral arrangement of the planets on only one half of the cir­cle. It lasts a long time and to make everyone happy I'm reproducing the one for next March 14th.

They rejoice in believing that the trilions of decimals ensure and re­in­force the conquest, unseeing that they are wrong from the 3rd digit onwards.
Pi is not just a collection of random digits.
pi is a journey; an experience; unless you try to see the natural poetry
that exists in pi, you will find it very difficult to learn.
Antranig Basman – www.bestmessage.org/happy-pi-day-quotes/
Having clarified the basics, nothing prevents us from keeping the π its usual value, as long as it is acknowledged 3.1446055110296931442782342932803, and reproduce the table with all its revealing meaning by appropriately re­plac­ing ¼π with the cor­re­spond­ing shorter notation.

Let then be the table for the three models, with π = 3.14460…
SQUARECIRCLETRIANGLE
base | radius¼π 0.5 1- Φ6
perimeterππ½π / Φ
areaΦ¼π(¼π)5

Still in doubt? Are these not yet sufficient arguments to validate that final de­ci­sive leap towards the most integral knowledge?
If this long exposition has fascinated you as it did me, remember that with the π at 3.1415 everything we are admiring would be just a dead letter.

However, if it leaves you sceptical, or closed in on your mathematical rigour, I want to offer you something that has astonished me too, in my case fa­vor­a­bly, but which however will never have an explanation.
Rather than astrology it's more about pure mathematics: an astrology Chart is only the result of calculating the celestial positions with respect to the e­clip­tic, and its interpretation does not matter here.
I have calculated two hypotheses that I submit, elaborated on the basis of abstruse parameters deriving from re-interpreting the figures 3.1415 and 3.1446, right in homage and in the wake of the formulation of Pi Day in 1988.
  1. It uses the first three to designate the month and day of the anniversary, institutionalized 21 years later at an international level.
  2. Similarly, I have adopted the following two figures to indicate the Hours and Minutes of the event, necessary for the purposes of the symbolic cal­cu­la­tion of the Card.
    If nothing else, it is the most coherent of the various numerical ma­nip­u­lations, proposed as folkloristic hypotheses to offer this pi day to the com­mu­nity.
With the geographical coordinates of the Exploratorium museum of science San Francisco, California, set at 37°48'5" North and 122°23'41" West on the -8 time zone, space and time are completed, and here is the com­par­a­tive per­spec­tive of the two computations:

Exploratorium museum of science – San Francisco CA

Pi day Ascendant horoscope

From some official longitude of the museum 122°23'51" I would have ob­tained 3°14'34", but not being able to know at which point in its vast area the event may have greater consistency, I experienced the most ap­pre­ci­a­ble and significant, if not even probable position for our case, let's say the icing on the cake, until we saw the 46".

In any case, it is the extraordinary nature of the 3°14' Ascendant that in truth can only leave you speechless: 1/21.600 possibilities, for an as­cend­ant at 3°14' of Aquarius, the zodiac sign that characterizes the ev­o­lu­tion­ary era long awaited for the precession of the equinoxes; whereas the as­cend­ant in Sagittarius does not have any particular meaning in the theme.
Not even its creator could have imagined so much.

Therefore, the spatial interval of ±10 seconds should not be confused with the temporal interval of -3 hours and 1 minute (the true critical deviation of 3.01‰, which loses just 46°(303-257), almost a pre-fixed signal in turn as a warn­ing) canceling this incredible standard.

If one can give prominence to the fact that Albert Einstein was born on March 14 – a fact that few posts fail to mention – it is worth considering that it was 1÷365 possibilities, while the one we are seeing by sticking to the first three digits of the ascendant, is 1÷21.600, in addition to the correspondence of the precessional Sign; if we then evaluate how much easier it is to obtain 46", we are at 1÷1.296.000!
Should I perhaps ask myself why just last night I watched a cheerful film from 1937 (“TOPPER”), whose Italian title is translated “The Way of the Impossible”, culminating in a hotel room number 314; or whether the English name pier, as the residence of the new Museum has an affinity with pi and pie?
As I said, it doesn't prove anything and will never have an explanation.
It is even inconsistent, since the aforementioned Museum headquarters was relocated in 2013, the Pi day conceived in 1998 and declared official in 2009; but here a cocktail is served between heterogeneous ingredients, symbols focused on the numerical and historical value of the figure, combined as in an unpretentious abstract puzzle, stimulated by curiosity following the pi day, but with an amazing and unsurpassable result.
There is undoubtedly something for all tastes!
It happened and anyone can reproduce it with the proper parameters and app.

Perhaps mathematics is not just the calculation and regulation of numbers made up of all undifferentiated digits, but conceals a metaphysical paradigm of values and events whose intimate connection escapes flat rational logic.

For my part and as a simple spectator I must however take note of how in­tense­ly this π has managed to involve none other than the people of math­e­ma­ti­cians in their feelings, from the enthusiasm demonstrated by hundreds of accumulated comments, to the inspiration of transforming it into a cake to be cut into slices every March 13th, as if for a timeless ritual.
I just wonder if this is due to its magical presence, or its elusiveness behind the scenes of a perfect circle… given that mathematics should not need prop­a­gan­da to con­firm itself.

Wishing you a happy Pi Day, with a fair pie forever!


April 2024

from the Divine Triangle to the Great Pyramid

Everything elaborated on this page can only lead back to the last, or rather the first, piece of this mosaic: validate the squaring of the circle, made impossible by our mathematics, even if implemented in three-dimensional reality by the builders of the Great Pyramid of Giza – from which all this research of mine began.
It is the first and most solemn implication of the qualities of the Divine Triangle to unify the two figures of circle and square at the same perimeter, lending to the circle its vertex, around which everything rotates, i.e. its height as radius, and the square to its base, so the perimeter of the square divided by the diameter of the circle will reveal the mysterious π.

An­to­nio A­lessi © The Watch Pu­blisher, 2003-24

[ back || or to the main page ]