Chapter 2: Octaves

A scaling ratio of 2:1 emerges from the quantized grid when you throw equilateral triangles into the mix.

It can be easily seen (and proven mathematically) that for each equilateral triangle, the inner (inscribed) circle is exactly half the radius of the outer (circumscribed) circle. 

Doing this, we get a BINARY PROGRESSION, aka the OCTAVE and infinite Nested Dualities.

Can you see the doubling (octave scaling) of concentric circles, each containing the six-petalled flower?

Question: What is Σ (1/2)^n ?(n=1,2,3..... ∞)
Answer: 1

Union of all nested dualities is unity!

Everything is polarised!

3D Isotropic Vector Matrix (IVM) when polarised (tetrahedrons converted to star tetrahedrons), creates a binary progression in the VE (12 around 1) geometry.

This oactave scaling can go on ad infinitum in both directions.

This is a true 3D fractal.

“The Universe is divisible by 2”

~ Buckminster Fuller

And there is a 12-fold symmetry in an octave. 

Now, let's see what's in between an octave.