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 |
$\blacksquare$