Thinking about pentagons and dodecahedrons – 5

The pentagon is a unique regular polygon (all of its sides are the same length, and all of its interior angles are the same).

The divine proportion. The pentagon is unique because it contains within itself the golden mean or divine proportion, which can be simply expressed in this way: take a line of any length and divide it unequally into two parts so that the ratio of the whole line to the larger part is the same as the ratio of the larger part to the smaller part.

Big deal? Well, yes, because it turns out that this proportion is one that we find in nature again and again, for example, in the spiral of a sea shell and the way in which plants unfold. It is also one of the most aesthetically pleasing proportions to look at, which is why the Parthenon at Athens has been so admired for centuries.

When you draw lines between the vertices of a pentagon, the result is the pentacle, a five-pointed star, which encloses within itself another, smaller pentagon. It is in this pentacle that the golden mean reveals itself several times.

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