Friday, April 21, 2023

Phi-Eye and the Golden Circles

Pencil and compass drawing, digitally altered
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“I see through my eyes, not with them.”
— William Blake


The Golden Cut (1:1.618...) creating the Golden Circles 
overlapping within the vesica piscis
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“You will know, as far as it is allowed to a mortal, that nature is from all points of view similar to itself.” — Pythagorus

George Leoniak’s discovery of the Golden Circles template and the many different geometric connections that it makes possible really starts to open the doors of the phi ratio relationships in a very consistent way in your connection with geometry—no matter what level you’re at. 

The template, consisting of series of phi ratio proportioned concentric circles, in either 2, 3, or 5-fold view, makes working with sacred geometry altogether a more easily expansive and insightful practice, not only in the capacity to discover and construct forms, but in its ability to integrate the interconnected meanings of the root relationships, ratios, and perspectives more simply and coherently.

The Golden Circles are like a meta-organizing pattern to see the whole field of sacred geometry anew through. Exploring them is like interacting with a type of psychoactive auto-didactical generative tool for catalyzing new geometric connections and epiphanies; it is a way of keeping geometry in check with both the absolute transcendent, its source, and also the dynamic of life and phi as it emerges and connects back to source; both with the One and all its emergent self-similarities.


Three Golden Circle views:

2-fold/square view

3-fold/hexagon view

5-fold/pentagon view

Overall I find this approach a more holistic way of exploring and understanding what sacred geometry is, you could say it literally puts the proportional dynamic, the life of phi into the Flower of Life, or what Keith Critchlow more appropriately termed the “Flower of Creation.”

The basic version of the Golden Circles Seed of Life pattern is a simple and elegant complement to the traditional Flower of Life pattern. The Golden Circle lattice is in phi proportion and fits in between the familiar central 6-fold petals of the Seed of Life and Flower of Life patterns, giving an interaction and overlap between √3 and √5 geometries, showing us a richer field of interconnected circles for new connections, coordinates, and potentials for forms to emerge.  

The Seed of Life & Golden Circles, 
(blue circles are phi ratio/ √5, red are √3 )

Golden Circles Flower of Life

Working with the Golden Circles method incorporates multiple views and construction methods, both in what it does for understanding and discovering accuracy in the various solids and polyhedra based on phi, and in how it uses both digital and traditional compass methods for exploring and checking accuracy and creation method, and also 3-D construction.

A good example of this is how the Golden Circles method corrects the popular Metatron's Cube method of constructing a true dodecahedron. The difference is subtle but once you see it you can't unsee it. The dodecahedron created from the hexagon view of the Metatron's Cube method is not just a perspective or perceptual issue, it's a fundamental problem because it's not made from even-sided pentagons, and definitely not proportional to phi ratios, and so it cannot be constructed into an actual 3-dimensional form. 

(Images from George Leoniak)

Metatron method compared with Golden Circles Method

Golden Circles method - Nested Dodecahedrons
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Engaging with this phi based method or key to further opening the secrets of the circles of the Flower of Life allows the sacred and symbolic aspects and the of the unity of geometry, or harmony of the constants, to emerge as internal insights into the eternal that happen when you do the work and make the connections and interact with the mystery and your own curiosity and creativity.


Below are some of the various polyhedra studies, created from using the Golden Circles template pattern and variations, discovered & taught by George Leoniak and Knew geometers at Knew Geometry — (check out more on his work, courses, and group here: — Knew Geometry Youtube — Knew Geometers FB Group)

"The world around us is a world of numbers—numbers that spell life and harmony. They are organized by the geometry of figures, all related to one another according to a sublime order, into dynamic symmetry.
Glimpses into this magnificent kingdom form the basis of all our knowledge and it seems that in this domain the ancient civilizations had gone further than modern science." 
— Paul Jacques Grillo, Architect (1960) 


Golden Circle Polyhedra Studies

Dodecahedron from Golden Circles with √2 radius circles

Truncated Dodecahedron from Golden Circles with 0.618 outer circles 

Icosidodecahedron from Golden Circles

Truncated cube from Golden Circles with √2 circles

Great Rhombicuboctahedron from Golden Circles with √2 circles

Rhombicuboctahedron from Golden Circles with √2 circles x2

Rhombicosidodecahedron from Golden Circles 

Truncated Icosahedron "Buckminsterfullerine" from expanding Golden Circles 

Rhombic Enneacontahedron inside Dodecahedron from expanding Golden Circles

Great Rhombicosidodecahedron from Flower of Life with Golden Circles x4

Great Stellated Dodecahedron Star Polyhedron from Golden Circles

Small Stellated Dodecahedron from Golden Circles

Icosahedron front view from Golden Circles


“The Golden Circles of Giza”

The Great Pyramids slope geometry at the Giza Plateau is in precise alignment with the Golden Circles or phi ratio based concentric circles (blue & pink), and in part they give the generative points for its construction and inner shaft angles ..


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