sacred geometry: 8 circles around 1 when circle radii are in phi ratio

[alchemikey]

i was playing around with some software called geogebra and came across an interesting correlation between the radii of circles when in phi ratios of each other:



seem to express the octave

[Etude in B Minor]

By my math the ratio of the circles should be sqrt(2) not phi.

[alchemikey]

the radius of the central circle is 987
the 8 surrounding circles radii = 610
the next 8 = 377 then 233 then 144 then 89 then 55 then 34

they are all fibonacci numbers

[Etude in B Minor]

OK, my error (posting too late at night!). I used a TAN instead of SIN. The correct (I think!) answer is that the ratio of radii is 2/sqrt(2-sqrt(2)) - 1 = 1.6131259, which is very close to phi = 1.618034, but not exactly equal to it.

[alchemikey]

thanks for figuring out the math on that relationship...i had a feeling it wasnt exactly phi...here's another one based on the same relationship:

[Unbound]

Makes me think of this that I made -

[alchemikey]