Definition:Golden Mean/Geometrical Interpretation
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Definition
Let $\Box ADEB$ be a square.
Let $\Box ADFC$ be a rectangle such that:
- $AC : AD = AD : BC$
where $AC : AD$ denotes the ratio of $AC$ to $AD$.
Then if you remove $\Box ADEB$ from $\Box ADFC$, the sides of the remaining rectangle have the same ratio as the sides of the original one.
Thus if $AC = \phi$ and $AD = 1$ we see that this reduces to:
- $\phi : 1 = 1 : \phi - 1$
where $\phi$ is the golden mean.