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Fibonacci Studies

Fibonacci numbers are the result of work by Leonardo Fibonacci in the early 1200's while studying the Great Pyramid of Gizeh. The fibonacci series is a numerical sequence comprised of adding the previous numbers together, i.e., (1,2,3,5,8,13,21,34,55,89,144,233 etc..)

An interesting property of these numbers is that as the series proceeds, any given number is 1.618 times the preceding number and 0.618% of the next number.

(34/55 = 55/89 = 144/233 =0.618) (55/34 =89/55 =233/144 =1.618), and 1.618 =1/0.618.

This properties of the fibonacci series occur throughout nature, science and math and is the number 0.618 is often referred to as the "golden ratio" as it is the root of the following polynomial x^2+x-1=0 which can be rearranged to x= 1/(1+x).

So that's were the fib # 0.618 comes from. The other fibs 0.382 and 0.5 commonly used in technical analysis have a less impressive background but are just as powerful in Technical analysis.

0.382=(1-.618)=(0.618*0.618)

and 0.5 is the mean of the two numbers.

Other neat fib facts (0.618*(1+0.618)=1 and (0.382*(1+.618))=0.618.

Use of Fibonacci Studies in Technical Analysis

Fibonacci numbers are commonly used in Technical Analysis with or without a knowledge of Elliot wave analysis to determine potential support, resistance, and price objectives. 38.2% retracements usually imply that the prior trend will continue, 61.8% retracements imply a new trend is establishing itself. A 50% retracement implies indecision. 38.2% retracements are considered nautral retracements in a healthy trend.

ABC's

Price objectives for a natural retracement (38.2%) can be determined by adding (or subtracting in a downtrend) the magnitude of the previous trend to the 38.2% retracement. After the 38.2% retracement the stock should break through the previous swing point(B) on heavier volume. If the volume isn't there the magnitude of the move will usually be diminished, especially on very low volume.

A-B =C-D when B-C =38.2% of A-B

Thus, Fibonacci numbers are a sequence of numbers in which each successive number is the sum of the two previous numbers: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, etc. These numbers possess an intriguing number of interrelationships, such as the fact that any given number is approximately 1.618 times the preceding number and any given number is approximately 0.618 times the following number.

This numerical relationship is named for its discoverer, Leonardo Fibonacci, who was an important mathematician born in Italy around the year 1170. It is rumored that Fibonacci found this relationship while studying the Great Pyramid of Giza in Egypt. There are four Fibonacci Studies used to analyze chart patterns: Arcs, Fans, Retracements, and Time Zones.

The general interpretation of the Fibonacci Studies involves the anticipation of a change in trend as prices near the lines created by the studies.