Reciprocal Form of One Minus Golden Mean

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Theorem

$\hat \phi = - \dfrac 1 \phi$

where:

$\phi$ denotes the golden mean
$\hat \phi$ denotes one minus the golden mean: $\hat \phi = 1 - \phi$.


Proof

\(\ds \hat \phi\) \(=\) \(\ds 1 - \phi\)
\(\ds \) \(=\) \(\ds -\left({\phi - 1}\right)\)
\(\ds \) \(=\) \(\ds -\frac 1 \phi\) Definition 3 of Golden Mean

$\blacksquare$