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\begin{document}
The golden mean is the number \[ \frac{1 + \sqrt{5}}{2}, \] that is the root larger in modulus of
\begin{equation} x^2 - x - 1. \end{equation} It is usually defined as the ratio of two lengths
\(a\) and \(b\) such that \begin{equation*} (a+b) : a = a : b. \end{equation*}
Let \(x\) be the ratio \( \frac{a}{b} \), we have \( \frac{a+b}{a} = 1 + \frac{1}{x} \),
from which we get the equation \(x^2 = x + 1\).
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