Golden Mean Solution

Set the long side divided by the short of
each rectangle equal to each other and
also equal to the golden mean G.
 a + ba = ab = G

Separate into two equations.
 a + ba = G    ab = G

Let a = 1, or b = 1, or solve right equation
for a or b or invert it. Substitue into left
equation. Below shows letting b = 1.
 a + 1a = G    a1 = G

Right equation shows: a = G.
Subatitue this into left equation.
 G + 1G = G (See note below)
 G + 1 = G²
 0 = G² - G -1

Use quadratic formula. Find positive root.
  G= 1+52 ≈ 1.618034
Note: Add subscrips to this formula to
create a fixed point formula.

 (Gn + 1) / Gn = Gn+1

Set G0 to a positive seed value. If set to
1 then ten iterations gives G10 ≈ 1.618.
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