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A beautiful phenomenon, mathematically speaking the golden ratio can be constructed and represented in many ways, for example it is the irrational constant that is the positive solution to the quadratic equation

𝜑2−𝜑−1=0.

This is an algebraic representation of the more well-known geometric definition, being the ratio between two sides of a ‘golden rectangle’.

Such that

Taking a step back from shapes and formulas however, this concept has existed in the natural world for many millions of years (or even trillions if you consider the entire universe) before the Greeks ever started defining it. Here are three of the most beautiful examples to reconnect with the ‘real-world’ golden ratio!

1. Flowers

The placement of seeds in the head demonstrates the pattern of the golden ratio, or more specifically the ‘golden angle’ in this case. If you were to place a seed, rotate the flower and place another and repeat this process rotating by the same angle each time, a pattern would clearly emerge. The optimal way in

which the seeds can be arranged in this manner, and the way that is observed throughout nature in flowers, is achieved by rotating by the golden angle – the smaller of the angles about a point that is partitioned in the golden ratio.

 2. Hurricanes

The large spiral seen flowing from the eye of a storm in a hurricane follow a recognisable pattern often associated with a spiral shell, both of which can be describer using the golden ratio!

3. DNA

The very program for life, a DNA molecule displays properties of the golden ratio. For each full cycle of the double helix, the ratio between height and length is 34:21. As both 34 and 21 are in the Fibonacci sequence then their ratio will approximate to 𝜑!