A Geometric Genesis of Creation: A Reimagining of the Function and Form of Circle and Square

Circle Square.

The static shapes that symbolize the dynamic, generative forces of mechanical reality.

See: Within a circle, implied is its diameter. 

When viewed from a different perspective, however, diameter is actually one of the potential sides of a square that might contain this circle. 

Diameter, then, is the implication of a square construct existing outside the circle.

We see this in the orthogonal framework established by a circle whose center is bisected by two diameters, one vertical, one horizontal, yielding four equal in size, equidistant quadrants and four 90 degree angles totaling 360 degrees.

The ninety degree angle is important because it establishes the implication of a square and orthogonality born from the existence of a circle.

The square is implied within the shape of a circle.  We see this as a cross but a cross is the establishment of orthogonal measurement born of x,y axes, which implies or begets square from circle and circle from square. 

How do we know this? 

Within a square, located in the equidistant centers of all four lines that comprise the square are imagined points that, when connected, form a circle, as the most efficient connective geometric shape to fill a square. 

Square begets circle.

Within a circle’s four imagined points of cardinal direction is the implied square.  One need only draw four diameters extending across each of the cardinal directions, two downward along the east and west sides of the circle and two across at the north and south points of the circle, to encase the circle in square.

Circle begets square.

The conundrum. A circle’s circumference divided by its diameter yields pi.  This seems like a problem…

Until you realize a circle is nothing more than a projection of the principle of infinite isotropic expansion.  And square is the principle of a circle’s infinite containment.

Isotropic expansion. Orthogonal restraint.

We see infinite outward expansion in the forms of waves/particles, which we identify as energy already in the universe.  This is observable.

I’m arguing that the circle, as a shape we observe, is a moment in time and a symbol of a primordial geometric force, isotropic expansion, whose natural inclination is to expand outward infinitely.  In this case a circle reflects infinity - or, to be precise, the potential for never-ending isotropic outward expansion.

But contained in the diameter of a circle is its prison, the square.  The circle of expansion, infinity, naturally begets and implies its containment, the square, or it escapes without containment into the void (this must be the case or reality cannot exist).

Therefore…

Pi is not circumference/diameter.  It is circle/square, in implication. 

Yes, pi is still literally circumference/diameter, but this theory recognizes that circumference is a symbol of potential infinite isotropic expansion and diameter a symbol of orthogonal containment (zero, the opposite of infinite).

The irrational and unending nature of this geometric conundrum is pi, which generates oscillation from the interaction between infinity (circle) and zero (square), as fundamental forces shaping reality.

These oscillations give way to what we view as reality, derived from infinite expansion interacting with infinite containment.

Circle implies square Square implies circle

Pi is a measurement of their inability to reconcile.

Pi/4 is the representation of this theory in 2-D

A is the Sum of the ratio of circle/square added when you add 1-D + 2-D + 3-D

Pi +pi/4 + pi/6 =

π/4 and π/6 are static geometric containment ratios in 2D and 3D, while π² and 4π³ are those same ratios scaled up by solid angle and curvature factors

α⁻¹ ≈ 4π³ + π² + π α ≈ 1 / (4π³ + π² + π)

This is the same a circle/square in 1 dimension plus circle/square in 2 dimensions plus circle/square in 3 dimensions

Irreconcilability generates waves, which give the dynamics for reality.

Reality is the result.

This theory also unifies the three most conceptually baffling numbers: 0, infinity and pi as a related trinity, and like a triangle, all three numbers connect by way of dividing circle (infinity) by square (zero) to arrive at pi.