Shells
This shape consists of rectangles in which the ratio of the sides ( ) is equal to the Golden Mean (Phi). This can result in an infinite nesting process, taking on the form of a spiral. It is called the logarithmic spiral, and can be found throughout nature. Snail shells follow the logarithmic spiral, as does the cochlea of the inner ear. It can also be seen in the horns of certain goats, and the shape of certain spider's webs.
Faces
Faces are full of examples of the Golden Ratio. The mouth and nose are each positioned at ‘golden sections’ of the distance between the eyes and the chin. The ear also follows along a spiral pattern.
Every person’s body is different, but the averages across populations tend towards ‘Phi’. It has been said that the more closely our proportions adhere to ‘Phi’, the more attractive those traits are perceived. As an example, the most beautiful smiles are those in which central incisors are 1.618 wider than the lateral incisors, which are 1.618 wider than canines, and so on. It's quite possible that we are primed to like physical forms that adhere to the Golden Ratio.
Mathematics can sometimes be considered as a somewhat dry subject, with limited relevance outside the classroom. However, as we have seen, mathematical patterns are all around us in nature. The intricate patterns often seen appear to be random on first inspection. However, Fibonacci’s genius was to delve deeper into these seemingly uninteresting sequences and find a hidden gem, or that ‘golden opportunity’.
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