Circle two
was the construction circle that makes up the inner part of the
spiral. I like to incorporate smaller elements as they often hold
the key to an important geometric statement. Incorporating usually
means tangents or crossings. From the vertical axis I expanded a
circle that tangented the inner small circle, the small circle
between the centre circle and the tail, and the tail. Then I
inscribed this circle, c2 in a larger circle. Then I had an idea to
find the spot on the spiral for the inner small circle and the
smallest circle close to the tail. Then I drew a line through these
two new placed circles which made a nice tangent to the inner circle
and pierced the centre of the last laid down circle in the spiral.
Then I drew two legs to the top of the vertical axis and checked the
degree of angles, which are 60 degrees on all three corners (marked
with red dots). I then looked for Phi, which was found as described
in the picture (extremely accurate).