In this video, I analyze the Bitcoin chart. Opinions on bitcoin tend to be very polarized. In this video I try to take a balanced view and simply look at the long term chart and where price is trending. I overlay this chart with Fibonacci and Elliott Wave analysis to arrive at the conclusion that...Read More

In this video, I analyze the S&P500 chart, which is now meeting up with 20-year long term resistance and the upper bound of its year long channel, but is also breaking out above the 261.8% Fibonacci extension from the 2007 peak to the 2009 bottom in equities.Read More

Picking up from last week's video, I wanted to do a deep dive into gold, particularly because there is a diversity of opinions regarding whether we break down from here or we make another leg higher. In this video, I address a recent chart from JC Parets at All Star Charts and my opinion regarding...Read More

In this week's video I take a look at the charts of gold, silver, platinum, palladium, and copper and offer some thoughts on where I see prices moving next. As always, whether you agree or disagree, I would love to hear your feedback.Read More

In this concise (less than 15 minutes total) 5-part video series, I provide a very brief overview of the subject matter, introduce the basics of applying Fibonacci ratios in technical analysis, and offer my opinions on why I think it works. I hope you find the videos informative.Read More

The run-up in gold this morning has price action testing the downtrend line from the September high for the fourth time. Gold has been forming a bull flag for the past eight weeks, and $1505 also coincides with the 38.2% Fibonacci retracement from the September high to the October low.Read More

Fibonacci refers to the sequence of numbers made famous by thirteenth-century mathematician Leonardo Pisano, who presented and explained the solution to an algebraic math problem in his book *Liber Abaci* (1228). The Fibonacci sequence and the ratios of its sequential numbers have been discovered to be pervasive throughout nature, art, music, biology, and other disciplines, and they form the foundation for Fibonacci trading tools. Traders apply these Fibonacci levels to help interpret market behavior and to isolate higher probability setups and market pivots.

The sequence begins with 0 and 1 and is comprised of subsequent numbers in which the nth number is the sum of the two previous numbers. The equation for finding a Fibonacci number can be written like this:

Fn = F(n-1) **+** F(n-2). The starting points are F1 = 1 and F2 = 1.

Each number in the Fibonacci sequence is identified with a subscript 1, 2, 3, 4 …… to indicate which term of the sequence we are talking about. Thus F16 refers to the sixteenth Fibonacci number.

Related to the Fibonacci sequence is another famous mathematical term: the **Golden Ratio**. When a number in the Fibonacci series is divided by the number preceding it, the quotients themselves become a series that follows a fascinating pattern: 1/1 = 1, 2/1 = 2, 3/2 = **1.5**, 5/3 = **1.666**…, 8/5 = **1.6**, 13/8 = **1.625**, 21/13 = **1.61538**, 34/21 = **1.619**, 55/34 = **1.6176**…, and 89/55 = **1.618**… The first ten ratios approach the numerical value 1.618034… which is called the “Golden Ratio” or the “Golden Number,” represented by the Greek letter Phi (Φ, φ). After these first ten ratios, the quotients draw ever closer to Phi and appear to converge upon it, but never quite reach it because it is an irrational number. Phi (Φ), 1.61803 39887…, is also the number derived when you divide a line in mean and extreme ratio, then divide the whole line by the largest mean section; its inverse is phi (φ), 0.61803 39887…, obtained when dividing the extreme (smaller) portion of a line by the (larger) mean. In the image below, the ratio of the smaller part of a line (CB), to the larger part (AC) – i.e. CB/AC – is the same as the ratio of the larger part, AC, to the whole line AB. Therefore, CB/AC = AC/AB.

Phi and phi are also known as the Golden Number and the Golden Section. The formula for Golden Ratio is: F(n) = (x^n – (1-x)^n)/(x – (1-x)) where x = (1+sqrt 5)/2 ~ 1.618 The Golden Ratio represents a fundamental mathematical structure which appears prevalent – some say ubiquitous – throughout nature, and is used as the basis for Fibonacci tools in trading.

Did you know you can download a FREE copy of *Master Fibonacci* with a free membership on Fibonacci.com?

Paperback: 128 pages

Author: Shelley Allen, M.A.Ed.

Publisher: Fibonacci Inc.; 1st edition (2019)

Language: English