28/_{32}

In fact, it can be said that these calculations are structured as oriented to the quarter of a circle, referring to the radius; something that should emerge spontaneously from the report already detected: √Φ × 4; a more enlightening perspective than taking into account the value of π at 360 ° – the view initialized by the multiple polygonal path's approach – and let's see why, this time in a more mathematical way.
To calculate the length of ¼ of the circumference, reflecting the properties of the square, just geometrically contrast the arc BD with the sum of 2 rays, CB and CD which define it, as base (the root) and height of the arch.
By applying to them, or graphically to the perimeter of the virtual square CBED from the vertex in C , the proportion √Φ , we will have obtained the new square Cbed , which intersects the two major sides (or radii: ×2r = 2×r ) defining with the sum of the new sides bC and Cd exactly the arc length BD .
BD = 2r ×
^{2}√Φ
BD = BA ×

CBED = r²
CBD = r² ×^{4}√Φ

To calculate the area of the quarter circle, since it is^{2}√Φ
the side of the square having the area of the entire circle, with the same procedure must be applied to the area of the single quadrant
CBED the^{22}√Φ
(0,88665177931216226…).
And here is the expected symbiosis of square and circle, deriving directly from the simplest and most practical formulation. A mystery that never existed.
on the diameter AB = 1 , that is r×2 ,
^{2}√Φ cut out the length of the
quarter of circumference BD; 

on the r adius BC already raised to ^{2} for the area BCDE,^{4}√Φ cut out the area of the quarter of circle CBD.

Regarding the two radii that delimit the quarter of a unit, their point of convergence for the circumference constitutes the center; their extremes the peripheral points of divergence, are valid for circle and square: to define all the other points equidistant from that center is precisely the square root of the only coefficient of numeral, spatial and gravitative equilibrium, which is the golden section.
To say the least, a stimulating as well as brilliant example of semantic correspondence, I would dare to say the more realistic if each term finds its right place, recurring the incidence of the 4 and the square as well as its square root at each step and subtle scan; even if it cannot be adopted by now, it is material for reflection on the real transcendent character of π.
Developing this conception of π, our earthly unit of measurement is proposed as the quarter of a 'turn', which has the same modular function as a [quarter of] square, but it expresses and links together with φ dynamism and growth; where the model is not for example the whole year, but the single season, each interaction manifests itself with greater likelihood.

