Intermediate and Advanced Technical Analysis Series
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Origins of Fibonacci – The “Golden Ratio”
The “Golden Ratio” is a special number, represented by the Greek letter “Phi” that is equal to approximately 1.618. The ratio can be used to explain many things in geometry, art, architecture and astronomy. The phenomenon appears in many natural events, ranging from small strands of DNA to the unimaginably large in galaxies such as the Milky Way.
The mathematical sequence was discovered by mathematician, Leonardo Pisano Bogollo, who lived in Italy between 1170 and 1250. His nickname “Fibonacci” roughly translates as “Son of Bonacci”.
The first two numbers in the Fibonacci sequence are 0 and 1, but then each subsequent number is the sum of the previous two. The relevance of the “Golden Ratio” to the Fibonacci sequence is that the further into the sequence you go, the closer the numbers increase by a ratio of 1.618.
In mathematical terms, the sequence Fn of Fibonacci numbers is defined by the recurrence relation and can be written as a rule mathematically:
Fn = Fn-1 + Fn-2
Figures 1 & 2: How the Fibonacci series develops and the first 15 numbers in the sequence