From sunflowers to galaxies, nature has a favourite number: 1.618. This is the Golden Ratio, and it shows up so consistently in the natural world that mathematicians, artists, and scientists have been fascinated by it for centuries. The Pyramids of Giza, the Parthenon, and Da Vinci's Mona Lisa all incorporate proportions said to be based on it. But here is the part that might surprise you: the same ratio has found a home in financial markets, where traders use it to try and predict where prices might turn.

The Golden Ratio comes out of the Fibonacci sequence, a series of numbers where each one is the sum of the two before it: 1, 1, 2, 3, 5, 8, 13, and so on. As the numbers get larger, dividing any number in the sequence by the one before it gets closer and closer to 1.618. The sequence itself is named after Leonardo of Pisa, a 13th-century Italian mathematician, though Indian mathematicians actually discovered it centuries earlier. The fact that cultures on opposite sides of the world independently arrived at the same ratio is very telling, as it kept appearing in nature regardless of who was looking for it. This is exactly why it has proven so difficult to dismiss as coincidence.

The connection between this natural mathematical pattern and human economic behaviour is not as strange as it sounds. Economists like Adam Smith and John Maynard Keynes both argued that people make economic decisions guided by something like natural instinct; Smith called it the "invisible hand," and Keynes compared it to the navigational instincts of migratory birds. In a sense, the Golden Ratio may be the mathematical expression of that same natural balance playing out in markets. When prices move, traders tend to cluster their decisions around the same widely recognized levels, and those levels, 38.2%, 50%, and 61.8%, all come directly from the Fibonacci sequence.

Whether the Golden Ratio works in markets because of deep mathematical truth or simply because enough people believe in it is still an open debate. Critics argue that with so many possible Fibonacci levels to choose from, prices are bound to bounce near one of them by chance. But that critique actually points to something worth sitting with! Even if the ratio works partly because traders make it work, the practical result is the same.  A number that has shown up in sunflowers, ancient architecture, and works from the Renaissance continuing to shape the way modern markets move is, at the very least, a pattern worth paying attention to.

Sources: https://www.academia.edu/89595164/Analysis_of_the_Golden_Ratio_Theory_in_Terms_of_Economic_Theories