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 $AD$.

GoldenMean.png

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.