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 refusedConcentrating 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.
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 reverseAn 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
but also that
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 √ Of course, a square with the same area as the circle will have the side = ^{4}√Φ 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 squarecircle 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.
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 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,
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 longedfor goal, but he lacks the key to access, since the key is precisely the π.
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.
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
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.
π The bubble would explode into a myriad of microdroplets, such as to suggest more than the 131k sidesegments of the last simulation polygon inscribed in the circle. Is it not likely that the molecular or even interatomic 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? 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 1516 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.\
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 φ^{2} 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/φ^{2} = 0.300… (with minimal approximation^{}, it's like saying area of the circle /φ^{2} , 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.
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
A truly unmissable AC is 0.5 ,
that of the smaller circle with diameter Φ^{3} , or in any case 0.5 × Φ^{3} ,
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 .
In fact, the remaining decimals are crumbs justified by the exact calculation of the golden section, which confirms an identical result, also by √Φ×Φ^{2} , 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:
.
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
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 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
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.

base  radius  π  0.5  √ 1 π^{12} 

perimeter  4  4  2 
area 
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 4π
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 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.
base  radius  ¼π  0.5  √1 Φ^{6} 

perimeter  
area  Φ 
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.
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.
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 (
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.Wishing you a happy Pi Day, with a fair pie forever!