forex™
Number theory – Technical Forex Analysis
Fibonacci numbers
The Fibonacci number sequence (1, 1, 2, 3, 5, 8, 13, 21, 34 ...) is constructed
by adding the first two numbers to arrive at the third. The ratio of any number
to the next larger number is 61.8%, which is a popular Fibonacci retracement
number. The inverse of 61.8%, which is 38.2%, is also used as a Fibonacci
retracement number (as well as extensions of that ratio, 161.8%, 261.8%). Wave
patterns and behavior, identified in Forex trading, correlate (to some extent)
with relations within the Fibonacci series. The tool is used in technical
analysis that combines various numbers of Fibonacci retracements, all of which
are drawn from different highs and lows. Fibonacci clusters are indicators which
are usually found on the side of a price chart and look like a series of
horizontal bars with various degrees of shading. Each retracement level that
overlaps with another, makes the horizontal bar on the side darker at that price
level. The most significant levels of support and resistance are found where the
Fibonacci cluster is the darkest. This tool helps gauging the relative strength
of the support or resistance of various price levels in one quick glance.
Traders often pay close attention to the volume around the identified levels to
confirm the strength of the support/resistance. 
Gann numbers
W.D. Gann was a stock and a commodity trader working in the '50s, who reputedly made over $50 million in the markets. He made his fortune using methods that he developed for trading instruments based on relationships between price movement and time, known as time/price equivalents. There is no easy explanation for Gann's methods, but in essence he used angles in charts to determine support and resistance areas, and to predict the times of future trend changes. He also used lines in charts to predict support and resistance areas.
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