Sacred Geometry Blog lesson #3

The Golden Proportion PHI is the hidden treasure of Sacred Geometry as well as the secret power harmonizing the cosmos.
Hereafter, we will refer to PHI by its symbol, the 21st letter of the Greek alphabet "Phi": Φ.

Φ is easily expressed as a comparison of similarities:

THE SMALLER IS TO THE LARGER AS THE LARGER IS TO THE WHOLE.

b : a :: a : (a + b)
or in words: “b” is to “a” as “a” is to “a + b”

Shown in a different way, below we have two Golden Proportions nested into each other
and forming a harmonic unity: on ruler AC, we have BC / AB = AB / AC. 

On ruler D, in terms of numbers, we have here 4 lengths (13, 21, 34, and 55 centimeters) in PHI proportion.
These lengths are part of the Fibonacci Series (see SG Blog lesson #2) which generates the PHI proportion.
These lengths create a harmonic cascade:

13 is to 21 as 21 is to 34 and as 34 is to 55
the very small is to the small as the small is to the large and the large is to the whole.

To help us see the Golden Proportion better, let us visualize the lines as circles or balls:

In the above drawing, the small ball (blue) is to the larger ball (orange)
as the larger ball is to the whole ball (red).

Now, if we rotate the above design 90º counter-clockwise, we get this:

The above shape is the most perfect and simple representation of the Golden Proportion. It shows the fractality of PHI as a Harmonic Trinity:
1 and 2 are nested into 3 as One. This PHI Trinity diagram is a template of nature and appears in famous historical examples:
• the “Arbelos” of Archimedes (c. 287 BC - c. 212 BC).
• the "Vitruvian man" by Leonardo da Vinci (1452 - 1519).
Both are based on PHi, the Golden Proportion. 

If we embed or “nest” the 3 circles into each other, we obtain an image of dynamic growth
where the small (blue) circle is in Phi ratio to the larger (orange) circle (at the Golden Point Φ1),
just like the larger (orange) circle is in Phi ratio to the whole (red) circle (at the Golden Point Φ2) etc...
Not only these circles are self-similar, which is a typical property of fractals, but they are Goldenly Self-similar:
they are called Golden Fractals. (See upcoming SG Blog Lesson #10) .

If we keep embedding the Phi-proportioned circles, we get a sense of endless harmony or infinite fractality.
The nesting pattern keeps repeating smaller & smaller, just like it could be manifesting larger & larger.
This is called Golden Fractality. 

 

End of Sacred Geometry Blog Lesson #3
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Harmony Blessings!