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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These above images are a 24 circle torus topology using the compressed Fibonacci sequence. The first image shows where all the 9s are (looking very similar to Phi spirals). The second image shows the compressed Fibonacci numbers moving around the centre and the third image shows the Fibonacci series spiraling into and out of the centre.
More visualizations to follow......
These are the other patterns highlighted in a convienient way - there are more, but if I highlight them all it gets hard to see what's going on.... The Fibonacci series has 24 positions with 12 being the inversion/mirror point and there are 4 circuits in the full 24 postions; There are 2 doubling circuits going in opposite directions and 2 spirit circuits except one of them is a polar number pair circuit (1,8,1,8,1,8) and the familiar 3,9,6,6,9,3.
I've highlighted all of these circuits in two different views each, as well as one way of looking at the FNGs and all of the 3,9,6,6,9,3 circuits.....all circuits go both around the centre and into it in a spire of one type or another.
That is a simply elegant way of looking at it Barbitone! I keep thinking of one of them as an ion and the other as an atom. :)
Riseball, thanks so much for all the neat geometries and link to the Janusz Kapusta article. When I noticed the reference to Jay Kappraff at the end, I kept thinking I had heard that name before and realized that it was during my studies of The Sacred Cut:
http://www.scribd.com/doc/59714586/The-Sacred-Cut
I have also put together some compilations of articles on Sacred Geometry for everyone:
http://www.scribd.com/doc/59885848/Sacred-Geometry-Notes-01
http://www.scribd.com/doc/59885866/Sacred-Geometry-Notes-02
http://www.scribd.com/doc/59885887/Sacred-Geometry-Notes-03
There is an endless amount of connections that could be made between these geometries and the physical structure of all things. I would like to share a few observations with you all, but will come back to it later.
This isn't Phi related but I dont want to start a whole thread for it, I just want to share it so I'll do it here;
Exponents of recipricols 2 and 5
Exponents of 2;
2
4
8
16
32
64
Exponents of 5
5
25
125
625
3125
15625
(Note; Exponents of 5 and halving are the same numbers only halving is 0.5, 0.25 etc....instead of just 5, 25 etc...)
What I want to share is this;
The difference between exponents of 2 and 5 are found by taking the smaller from the larger, so;
5 - 2 = 3 (3)
25 - 4 = 21 (3)
125 - 8 = 117 (9)
625 - 16 = 609 (6)
3125 - 32 = 3093 (6)
15625 - 64 = 15561 (9)
The difference between exponents of 2 and 5, when compressed to single digits, are the emenation circuit 3,3,9,6,6,9. I have never seen anyone point this out before. I was wondering how exactly to show how this sequence comes about besides simply mirroring the original 3,9,6 and came up with this....
Now if someone asks you why is it 3,9,6,6,9,3 you can show them this among other ways.....
Not only that, powers of ten come about when you multiply the exponents of 2 with the exponents of 5;
2 x 5 = 10
4 x 25 = 100
8 x 125 = 1,000
16 x 625 = 10,000
32 x 3125 = 100,000
64 x 15625 = 1,000,000
4 and 7 are different because they produce FNGs of 1,4,7 - the difference between them in this case is 3,6,9,3,6,9....
whearas 2 and 5 produce the doubling/halving circuits.
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