Since gravity is spherical, and the true π is the one that determines the spher­i­cal curvature starting from ()² of any radius, thus translating from the Cartesian axes to a 3-dimensional system xyz (conceived as Eu­clid­e­an space), it (the π agent) is a vector of the 4th dimension, the grav­i­ta­tion­al agent which, as a factor of conversion from Euclidean dis­cre­tization to spher­i­cal isotropy, prelude or supersedes the ordered den­si­fi­ca­tion of mat­ter, with the gravitative equilibrium enabling the po­si­tion­ing and motion of masses, from particles to celestial bodies; and slowing down the vi­bra­tory level [of the Universal Creative Con­scious­ness] to the frequency of the di­men­sion visible and practicable by us; slowdown that triggers the ‘round­ness of time’, as a function of the ro­ta­tion­al attributes and cyclicality in the evolutionary space granted to us.
“Your entire universe manifests the differing frequencies of vibrations
of consciousness energy particles.
As these frequencies move up or down from one level to another,
so do the visible and physical structures manifest differing levels of energy
and there is a change of mental patterns and emotions and appearance.”
CHRIST's LETTER n.3 – page 112, ¶3.108dictation 1999.
From a mathematical perspective, and if you like as a heuristic approach, I would therefore like to be able to consider it as the threshold – or transit element – between Euclidean [abstract] and non-Euclidean [concrete] space. I take it up and associate it with the term ‘element’, since it reminds me of the idea of Fire, which unlike Earth, Water and Air is not subject to gravity, having no mass or size of its own, but interacts as such with the mass of others three, transforming it both from the inside and from the outside, and regulating the dynamic balances of par­ti­cles by acceleration or inertia, expansion and con­trac­tion, attraction or repulsion.
It is the function that appears to be recognized at the constant 0.78615­[137­775742…] = Φ.
An essential fourth dimensional argument, basic circle~square integration, which is projected in four directions and modalities inherent in the sphere.
With it, from the arc 2r×π to the area of the right sector π×r², ×4 here is the area of the circle; which ×4 gives the area of the spherical surface, which ×4 is the base area of a cone which at height r has the volume of the sphere.
I wish to stress again that starting from the quarter-circle sector, that is from the quadrant cut out from the single π applied to the virtual geometric square of the radius, results more significant than one might imagine at first sight for the whole calculation process, since the recursivity of the '4' connectes each step in an extremely easy and intuitive way. And it is no less in the formation of spirals.

Seen in this way, the π it manifests itself in concert with the golden spi­ral (not always easily identifiable, giv­en complex gravitational in­ter­ac­tions), to give life to complex phe­nom­e­na and structures in evolution.

The images reproduce the Milky Way Galaxy, to which I have superimposed an exact double golden spiral (not the one generally passed off as such, which would lead nowhere… see pages 10,11), and a second one from golden circles (p .26). Despite the inclinations of recovery, the progress appears clear.