Vortex Based Math

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I thought I'd start this thread for all our Phi related findings, of which I have been finding a few lately. As soon as I started using powers of Phi, I found many things.


One of which is this;So the middle of a line which is sectioned 1.618, when a circle from the centre to the Phi point is scaled up by cubed Phi (4.236), defines the full line diameter.


What I was, and am looking for, is the connections between Phi/powers of Phi and doubling/halving/powers of 2. I believe that these two functions are recipricol in some way and are both exremely profound ratios. Phi, I believe, is the key to the torus shape and the fractal torus skin iterations/macro-micro expansion contraction...whereas the 64 Tetrahedron grid/Flower of Life/doubling-halving/powers of 2 are all about the sphere - a container, a matrix, a boundary....


I was particularly interested when I found this correlation between the flower of life/vesica/doubling-halving and CUBED Phi, because I am looking for 3D scaling. For instance, as Walter Russell points out also, to make a new "1" (sphere) you need 8 parts, as in, the seed of life in 3D is 8 spheres creating a new equalibriam, or 8 Tetrahedrons (Star Tetrahedron).  (1,8,1,8,1,8) (1,8,64,512,4096,32768)


1 and 8 are recipricol in the sense of cubing and are of course mirror pairs (the 2 directions,+/-, on a single axis). I have a strong feeling that this is why, when the Fibonacci series is compresed to single digits, and the VBM circuits are found, there are 2 doubling/halving circuits (in opposite directions, one emanation/spirit circuit and an extra circuit of 1,8,1,8,1,8 that mirrors the emenation circuit. So it is similar to the emanation circuit in some way... I have a feeling it has something to do with a dimensional scaling axis (macro/micro).

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I have been investigating the relationship of PHI, DOUBLING CIRCUIT, polygons, CIRCLE, SQUARE & TRIANGLE.  They are all connected quite cleverly.  Also, I've been looking in to the relationship with the TWELVE.  Note the below picture has TWELVE SPOKES in the CIRCLE, and the baby phi (0.618...) sits right between the spokes, sorry there are no dimensions, the square is always 1x1 square to form the PHI and DOUBLING progressions.




Then an interesting occurence, you can make a SEED OF LIFE here like in SACRED GEOMETRY.  SIX CIRCLES around ONE, and they all fit the spokes of the 12 in the 1x1 CIRCLE, and all the SHADED CIRCLES are all 1/phi^3 (0.2360679774997897) this is EQUAL TO (sqrt5-2).


Nice one Dean, a bit complicated looking at first glance, but I'll chew through it eventually.... :) Could you comment on what your thoughts are concerning the relationship between the doubling/halving circuit and Phi ratios? Can you boil it down a little into words for us?



Taking a circle and using the radius of where it INTERSECTS THE LINE, an interesting thing happens, THE GREEN CIRCLES ARE ALL THE SAME SIZE (1/phi^2) and two of them fit that circle perfectly.



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