# Fibonacci

**Hardroners**

**Introduction**

Leonardo Fibonacci da Pisa is a thirteenth century mathematician. He discovered the Fibonacci sequence. And he switched, in the 13th century, from Arabic numbering to the arithmetic numbering. For his work in mathematics, Fibonacci was awarded the equivalent of today’s Nobel Prize.

**Fibonacci Summation Series**

The Fibonacci Summation series is discovered bu Leonardo Fibonacci. The rule is easy. This series takes 0 and adds 1 as the first two numbers. Succeding numbers in the series adds the prvious two numbers and thus we have 0,1,1,2,3,5,8,13,21,34,55,89,144 to infinity. If you divide a Fibonacci number with another previous Fibonacci number you will find the Golden Ration (1.618033). For example, 144 divided by 89 is near of the Golden Ratio.

**Fibonacci Ratio Table**

Different Ratios can be created in a table shown. How ? you need to take two Fibonacci number and divide. These numbers are everywhere and appear in nature and in the financial markets. You can find it in different structure of tree branches, flower petals, art, architecture …

- 1.618 is derived (in yellow) by dividing any Fibonacci number by another Fibonacci number that is found 1 place before. For example, 55/34 is around 1.61764. “
*1.618 is the Golden Ratio.”* - 0.618 is derived (in green) by dividing any Fibonacci number by another Fibonacci number that is found 1 place after. For example, 55/89 is around 0.61797.
- 0.382 is derived (in blue) by dividing any Fibonacci number by another Fibonacci number that is found 2 place after. For example, 55/144 is around 0.38194.

**Fibonacci Retracement/Extension**

- Retracement : Fibonacci retracement is used in technical analysis and associated with Eliott Wave to a market correction. This retracement will predict, with key Fibonacci levels, the area of support or resistance denoted. Then, the market will resume in primary direction.
- Extension : Fibonacci extension is used to determine their target profile into the areas of support and resistance. it refers to the market moving with the primary trend.