Sacred Geometry derives from the primal act of the Division of Unity
∆ represent the transformative principles.
Division of Unity: Pi/∏
From undifferentiated Unity (circle) creation occurs through an internal division of unity, the primal act, since there is nothing outside, God creates within itself, the finite reality (the diameter of the circle). In duality the possibility of existence, then form and multiplicity. The diameter is related to the Circumference by π, irrational…God is never quite resolved in finite terms.
The relationship between the diameter and circumference of the circle represented the teaching of the inner and the outer…the soul and the body…the idea and manifestation.
Tai Chi: divides unity such that each half is the whole as the circumference of the whole=the perimeter of the halves.
The diameter then equals the circumference. thus there is no separation from Unity and in the limit of expression differentiation merges into Unity
Guage Theory: creation arises from the breaking of symmetry.
Unity represented by circle, square, triangle, pentagram/double square. The division of these yields:
π, √2, √3, √5 and ø defines the basic symmetries in nature
√2, √3, √5=Triad of Transformative Principles.
These are all that is needed to define all the forms in nature.
If the form/manifestation is knowable-rational, the diagonal or the root is the irrational, the unknowable.
Where whole numbers, integers represent states of being, qualities in existence, symbolize creative principles or Laws: the sacred roots symbolize process…the dynamic.
The principles of 1) multiplicity/generation- 2)formation-and 3) transformation/re-generation.
Transcendental Numbers: the “irrationals” numbers or √ roots are incommensurate: cannot be resolved into whole numbers…go on infinitely.
π does not repeat-has all patterns of numbers
Pythagoras called the incommensurable numbers “un-utterable”, the “alogon”, the “formless” because they represented the creative power of expansion which itself was un-utterable. Pythagoreans were sworn to secrecy not to reveal the existence of the alogon.
∆ the transcendentals, irrational numbers define the relationship of the finite (material) to the infinite (spirit) or to the Absolute through a discontinuity. The paradox is resolved in geometry ie pattern.