Why force the spiral circle approach? since each explains the other, the alternation is progressive; it is a cyclic expression based on the symmetrical flat circle, although this represents it in a more static way.
While the square then rises the function of measuring unit and module also in evolving spiral of the golden section, virtually reflecting in its same quarter for the area but also for the implications of the side (¼ of the perimeter and radius of the arcs), and thus attracting to it the quarter of a circle instead of the whole,
[our] triangle seems instead to perform a function of catalyst between the circle and the square, being itself totally and directly, without additions or derivations, 100%
In fact, the two sides of the triangle matching two quarters of a circumference, are like the perfect expansion of its base at φ: it is the unit that splits; or vice versa half of the base is Φ of each side.
The most significant finding is that only through this triangle, having developed the golden section thanks to the square, is it possible to trace the properties of the circle. A
Awaiting trialI know well that all this may not be shared by many, or all together; but it is now undeniable that the Divine Proportion is at the root of tangible reality.
It is undoubtedly the
There is no π endowed with phantom transcendence – unless by transcendence we mean the dead end to which its current definition has landed with an endless succession of almost completely useless figures.
What are they good for if they can't be integrated into calculations?
It is fundamental to take note that the problem of transcendence denounced by Lindemann, and which everyone boasts as if it were a way to reinforce the definition of the π, actually not only precludes the manual squaring of the circle, but equally applies to its numerical function, precisely because it cannot be represented in any algebraic equation with rational coefficients.
Put simply, while we will always be able to insert the value of Φ as
Incidentally, if it's any consolation, not even Leonardo da Vinci was able to fully apply the golden ratio to his Man of Vitruvius (a false ideographic examined and resolved in 2019, in the second part of the special site dedicated to the Great Triangle); and even less the relationship between the resulting circle and square, both geometric and symbolic – although it seems to be honored by that as if it were a hologram projected into space – in an emblematic function almost opposite to what it should have been.