The Fibonacci Sequence

Leonardo Bonacci lived in the 12th and 13th centuries and goes by many names. Long after his death, a historian branded him Fibonacci, which has since been his most famous moniker. Many people think of him as the best mathematician of his time. His most famous work is the Fibonacci sequence.

The first 14 terms of the sequence are below, as written by Fibonacci:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377

Later zero was added as the new starting point. Each number consists of the previous two added together. 1+1=2, 2+1=3, 3+2=5 and so on. Using this pattern, you can keep the sequence going beyond these 14. Although Fibonacci is credited with the sequence, it may historically originate from India. The pattern supposedly first appeared with two Indian mathematicians in 200 BC and 700 AD.

If you compare any number to the previous one, the ratio approaches The Golden Ratio (known by the symbol phi 𝝋). For instance 8/5=1.6, 13/8=1.625, 21/13=1.61538, and 34/21=1.6190. Each of these amounts gets closer than the last to 𝝋. It is equal to 1.61803 (rounded to five digits). You can calculate it as 𝝋 = (1+√5)/2.

Making squares with lengths the sizes in the pattern gives the golden spiral, as seen here:

Fibonacci showcased it by measuring rabbits’ population growth under perfect conditions in his book Liber Abaci. People have pointed it out everywhere in nature. Branches on a tree, pinecones, flowers, shells, spiral galaxies, hurricanes, and even DNA exhibit patterns of the Golden Ratio. Some say Leonardo and other famous artists included it in their work.

Uses for The Fibonacci Sequence

This number has not escaped the market’s notice. In Earn2Trade’s lessons, you will find us mention the Fibonacci sequence repeatedly. That’s because traders use a tool called Fibonacci Retracement Patterns. Using the 61.8% level and a few other key levels, you can see patterns in trading data.

This concept was taken to a dramatic place in a movie about mathematics and market analysis called Pi. It is the first movie by acclaimed director Darren Aronofsky. Pi deals with several theorists gaining a deep understanding of the Golden Ratio, with implications for finance and religion. It was released in 1998 on a small budget. Some believe it was the first movie ever to be available for download online.

Next time you see a spiral, remember the beauty of math and nature in the Fibonacci sequence. Also, keep in mind it can give you insights that help your trading, or  — if you believe Pi’s fiction — even give you a religious epiphany.