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'Golden Ratio' printed from http://nrich.maths.org/
The 'divina proporzione' or golden ratio, represented by the Greek
letter phi, is derived from the equation below where $a$ and $b$
are parts of a line.

$a+b:a=a:b$
i.e. $ \frac{a+b}{a}=\frac{a}{b}=\Phi\ \quad $(phi)

If $b = 1$ show that
$\Phi = a = (\sqrt 5 + 1 )/2 = 1.618034...$.
In the following equation
what does $x$ equal?
$$\Phi^{\left(\Phi^x\frac{x1}{\Phi}\right)}\frac{1}{\Phi}=x$$