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The Fibonacci Sequence

The Fibonacci Sequence Picture
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Leonardo Bonacci lived in the 12th and 13th century, and goes by many names. Long after his death, a historian branded him Fibonacci, which has since been his most famous moniker. He is said to be 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 first term. Each term consists of the previous 2 terms added together. 1+1=2, 2+1=3, 3+2=5 and so on. Using this pattern you can keep creating new terms beyond these 14. It first appeared with two Indian mathematicians, in 200 BC and 700 AD.

If you compare any term to the previous term, 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). It can be calculated as 𝝋= (1+√5)/2.

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

Fibonacci showed it measuring the population growth of rabbits 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.

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

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

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

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