Definition:Golden Mean/Geometrical Interpretation

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.