The following figure points out that like the circle 3 fills the distance from below the triangle’s base, to bottom of the outer circle 1, the circle 2 does the same on to the other side from above the base, which shows us with ease that the height of the Triangle
is even in Phi ratio with the outer circle diameter!
This revealed an alternative way to draw the complete golden triangle - all its sides being involved - and instructs us of many interesting detais concerning the relations between our ‘elementary’ rectangle and the concentric circles scaled in Golden Ratio, which look like to have beeen present behind the scenes at each step of our process, giving rise to what we can settle from now on as the “Golden Circles Ratio”.
|the Kepler's cite “division of a line into extreme and mean ratio” it was thus overcome,
as not only linear.
In deed a golden expansion map
is defined by a sequence of concentric waves, whose diameters are regulated by increase of the golden ratio j power – tap the figure if HTML.
The next step discloses one still unknown golden spiral, which works out through this plan, ie. crossing every circle at the same [zero] degree.
Our Great Triangle handles all these and much more, like a gate between the plain formulas and the revolving energy!