# Fibonacci Numbers

Fibonacci Numbers

Overview

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 #’s 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

61.8% retracements are warning signs of a potential trend changes. For a more detailed explanation of Fibonacci price projections and price wave theory I highly recommend the Elliot Wave Principle.

Confluence:Confluence occurs when you take fibonacci projections off of multiple trends and get the same number and strengthens when it corresponds with other technical advents such as gaps, swing high/lows, chart indicators crossovers (MACD, RSI, Stochastics, etc.), trading congestion, etc. The more confluence, the more significant the level. I really take notice when I get two or more fib #s (say a 38.2% and 61.8%) to correspond with a gap in the chart or a swing high. Confluence is very powerful as it combines multiple technical analysis techniques to arrive at the same conclusion, and should be relied on accordingly IMHO