a glass goblet against a crystal… at first glance they look the same, but a slight toll will reveal a dull sound against a tinkling one; for those in the know, it recalls the confrontation between reproduction of analog or digital sound.

Assuming the value of π/4 = VA = 0,786151 [previous figure], the contents of this figure, hyperniated on a circle with a diameter of 1m. and on a magical in­scribed triangle, they authorize clear and priceless connections.

 La QUADRA finita

With the center in V, trace an arc with a radius VA = π/4 until we meet in U the extension of the vertical axis CV.
We will have added to the unit-diameter LV the length of the side of which we will obtain the square root (with all due respect to F. von Lindemann).

Center on the midpoint of LU, the semicircle with this diameter is traced, which from point V can be intersected in S thanks to the perpendicular to LU.

For the properties of the right triangle defined by LUS [VU:VS = VS:VL], given VL = 1, it will be VS = VU ie of VA, and since VS² is the desired area of the circle with diameter =1, it is the same numerical value of VA to provide it in quadratic form.
In fact if r = ½ | πr²= π/4 | π/4 = VS
  1. /4)² = Φ  ergo  π = Φ×4
  2. (π/4 /2)² = πr²/4 = 0,19634954084936207740391521145497
  3. (πr²/2)² = πr²/4
  4. Φ×4r² = πr² che è Φ×1 = πr²
  5. a last important affinity: the side AV has the same length av given by the in­ter­sec­tion of the sides of the triangle with the horizontal diameter of the circle. This will lead to a further and to say the least simply u­nique a­nal­y­sis, de­vel­oped at astrotime.org, so much as to propose a sort of math­e­mat­i­cal π ge­ne­al­ogy.
The global error? If I may, we have tried by every means to penetrate the bound­a­ries of a single circle by sticking to the circumference, but ne­glect­ing its beating heart, from the center to the periphery, which could reveal the golden section.

The scenery

In examining what could prove to be the only legitimate solution to π, a pre­dict­a­ble scenario arises, based on three possible reactions:
  1. the mediocre one: this is a purely coincidental correspondence.
  2. the scientific one: it is necessary to re-verify the methodologies applied to the definition of the π, acquiring if and to what extent the incidence of a ‘Co­ef­fi­cient of Curvilinear Constancy’ can be traced back to the difference de­tected.
    After all, it will also be thanks to the efforts made to date if we can finally i­den­ti­fy and welcome a proven and definitive value of π, not transcendent but resulting from an algebraic equation.
  3. the intuitive one: there is no need for verification, as the criticism can be con­sid­ered well founded; reliable, necessary and sufficient the formulation of Φ×4, and therefore crucial and decisive.
    It remains to be settled whether as an act of faith the greater is this, or that of those who believe in the current default of π.