• Fibonacci Series
• Golden Ratio
• Fibonacci for Supports
• Fibonacci for Resistances

## Leonardo Fibonacci • The “greatest European mathematician of the middle ages”
• He was one of the first people to introduce the Hindu-Arabic numeric system into Europe
• He created the famous Fibonacci series

## The Fibonacci Series • Fibonacci series is a unique series of numbers
• Each number is the sum of the previous two numbers

## Golden Ratio • On any given line we have a unique point in the way it divides the line
• b/a = a/a+b = 0.618
• The result of the division is the Golden Ratio
• Denoted as the Greek Letter Phi

## Golden Rectangle – Golden Spiral • A golden rectangle is based on the Phi Ratio
• The relationship between its two sides is the number Phi
• Using this golden rectangle we can create a golden spiral

## PHI in Nature • Branches and roots extend based on Fibonacci numbers
• The golden spiral is seen in sea shells
• The golden spiral is seen in Hurricanes
• The golden spiral is seen in water

## PHI in The Universe • Phi can be found in space
• This galaxy follows the shape of a golden spiral

## PHI in the Human Body • Body measurements are based on Phi
• Even our DNA is made of golden rectangles

## PHI is Everywhere

• Φ is everywhere around us
• Do you think we can not find it in the financial markets?
• Prices find supports and resistances at the Fibonacci ratios

## Fibonacci for Supports in an Uptrend • For supports
• Draw Fibonacci from the ATL to ATH, from left to right
• Use the 23.6%, 38.2% and 61.8% levels for potential supports

## Fibonacci for Resistances in an Uptrend • For Resistances
• Draw Fibonacci from the ATH to last bottom, from left to right
• Use the 161.8%, 261.8%, and 423.6% levels for potential resistances

## Fibonacci for Resistances in an Downtrend • For resistances
• Draw Fibonacci from the ATH to ATL, from left to right
• Use the 23.6%, 38.2% and 61.8% levels for potential resistances

## Fibonacci for Supports in an Downtrend • For Supports
• Draw Fibonacci from the ATL to last top, from left to right
• Use the 161.8%, 261.8%, and 423.6% levels for potential supports