Phi³ [calc. Windows] = 0,23606797749978969640917364616882
CD = (Phi³ /2) = 0,11803398874989484820458682308441
(Phi³ /2)² = 0,01393202250021030359082632860559
(0,25 -(Phi³ /2)² = 0,23606797749978969640917367139441
with which we can choose between two formulas:
VA = AD × Φ
VA = √AD²+VD²
Apart from insignificant differences in calculations beyond the 25th decimal,
the square of a side
VA² is equivalent to the linear measure
VD, height of the triangle, which is Golden Section of the circle [diameter] as well;
but what has polarized and concentrated all my resources in this work is the realization that
VA is the real module, the tuning fork that makes all the strings of the mathematical system vibrate in perfect and eloquent harmony,
surpassing the fourth part of the π computed to date for only 0,00075….
While trying immediately to discover the underlying motivation, this leads us to believe and not without reason, or definitely means that the perimeter of the square with side
π [in the current project] is precisely:
and that therefore with
VA supervenes – ideal lemma in this case – none other than the rectification virtual of a quarter of a circumference
Furthermore, since the length of its side represents in sq. the area of the circle with diameter
mt.1, it will not be difficult to trace the square without the need for any calculation; although at this point the historic milestone appears to me as the least significant achievement of all, since:
we would have identified the
that is, the essential and existential entity, which modulates in the cardinal directions of space the ineffable detached balance, without gain or loss, of the eternal present, by virtue of the golden property on which it draws.
A magnificent fact, which informs the whole family of numbers and symbols in mathematics and geometry of new but eternal relationships between the atavistic formulas, charging them with an unprecedented synergy in the scientific path.
Suffice it to note that for the side of the large triangle, which in the circle with a diameter of
√Φ, represents with
mt. 0,78615… the side of the square perimeter, or ¼ of circumference, and with
sqm. 0,78615… the area of the circle.
It means that according to these clarifications of a π geometric ie " native"
the circle maintains a special Golden Ratio with the circumscribed square!
An extraordinary chain of deductions derives from this, which scholars will not fail to expand (one of which is already in existence at the “Journal of Modern Physics” and reported below);
but by now the primitive ratio of the circle with the square that contains it can be very illuminating, if not evidential: