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Fibonacci

Fibonacci in Nature: The Golden Ratio and the Golden Spiral

The more you learn about Fibonacci, the more amazed you will be at its importance

By Elliott Wave International

If you’ve studied the financial markets, even for a short time, you’ve probably heard the term “Fibonacci numbers.” The ratios and relationships derived from this mathematical sequence are applied to the markets to help determine targets and retracement levels.

Did you know that Fibonacci numbers are found in nature as well? In fact, we can see examples of the Fibonacci sequence all around us, from the ebb and flow of ocean tides to the shape of a seashell. Even our human bodies are examples of Fibonacci. Read more about the fascinating phenomenon of Fibonacci in nature.


Let’s start with a refresher on Fibonacci numbers. If we start at 0 and then go to the next whole integer number, which is 1, and add 0 to 1, that gives us the second 1. If we then take that number 1 and add it again to the previous number, which is of course 1, we have 1 plus 1 equals 2. If we add 2 to its previous number of 1, then 1 plus 2 gives us 3, and so on. 2 plus 3 gives us 5, and we can do this all the way to infinity. This series of numbers, and the way we arrive at these numbers, is called the Fibonacci sequence. We refer to a series of numbers derived this way as Fibonacci numbers.

We can go back to the beginning and divide one number by its adjacent number – so 1?1 is 1.0, 1?2 is .5, 2?3 is .667, and so on. If we keep doing that all the way to infinity, that ratio approaches the number .618. This is called the Golden Ratio, represented by the Greek letter phi (pronounced “fie”). It is an irrational number, which means that it cannot be represented by a fraction of whole integers. The inverse of .618 is 1.618. So, in other words, if we carry the series forward and take the inverse of each of these numbers, that ratio also approaches 1.618. The Golden Ratio, .618, is the only number that will also be equal to its inverse when added to 1. So, in other words, 1 plus .618 is 1.618, and the inverse of .618 is also 1.618.

This is a diagram of the Golden Spiral. The Golden Spiral is a type of logarithmic spiral that is made up of a number of Fibonacci relationships, or more specifically, a number of Golden Ratios. For example, if we take a specific arc and divide it by its diameter, that will also give us the Golden Ratio 1.618. We can take, for example, arc WY and divide it by its diameter of WY. That produces the multiple 1.618. Certain arcs are also related by the ratio of 1.618. If we take the arc XY and divide that by arc WX, we get 1.618. If we take radius 1 (r1), compare it with the next radius of an arc that’s at a 90° angle with r1, which is r2, and divide r2 by r1, we also get 1.618.

Now here are some pictures of this Golden Spiral in various aspects of nature. For example, on the left is a whirlpool that displays the Golden Spiral and, therefore, these Fibonacci mathematical properties. We also see the Golden Spiral in the formation of hurricanes (center) and in the chambered nautilus shell (right), which also happens to be a common background that Elliott Wave International uses for a number of its presentations and graphics.

We can also see the Golden Ratio in the DNA molecule. Research has shown that if you look at the height of the DNA molecule relative to its length, it is in the proportion of .618:1. If we look at the components of the DNA molecule, there is a major groove in the left section and a minor groove in the right section. The major groove is equal to .618 of the entire length of the DNA molecule, and the minor groove is equal to .382 of the entire length.

This graphic of the human body also shows how the Golden Ratio exists in certain relationships of the human anatomy.


Learn How You Can Use Fibonacci to Improve Your Trading

If you’d like to learn more about Fibonacci and how to apply it to your trading strategy, download the entire 14-page free eBook, How You Can Use Fibonacci to Improve Your Trading.

EWI Senior Tutorial Instructor Wayne Gorman explains:

  • The Golden Spiral, the Golden Ratio, and the Golden Section
  • How to use Fibonacci Ratios/Multiples in forecasting
  • How to identify market targets and turning points in the markets you trade
  • And more!

See how easy it is to use Fibonacci in your trading. Download your free eBook today >>

Dow and S&P Update: Can We Keep Going Higher?

by Adam Hewison

We owe trillions of dollars, but Crude oil is at $86 a barrel, the DOW, S&P, and NASDAQ are making new highs almost everyday and unemployment is officially at 9.7%.

Everything is great! Happy days are here again… Right?

So is the DOW, S&P, and NASDAQ all going to keep going higher forever? Or are the teachings of a dead mathematician going to reverse this juggernaut of a market?

In my new video I show you exactly what I mean and how the these indices could be very close to a very important tipping point.

Watch the Video: Can we keep going higher?

This is without a doubt, one of the most important videos I have ever made and if you are concerned about your financial future, you don’t want to miss it.

Fibonacci Techniques for Math Geeks – and Everyone Else, Too

By Editorial Staff

The word Fibonacci (pronounced fib-oh-notch-ee) can draw either blank stares or an enthusiastic response. There’s hardly any in-between ground. But for those who ask how an esoteric mathematical relationship can apply to price charts and trading, here’s a quick lesson. Everyone who uses Elliott wave analysis will sooner or later want to try using Fibo techniques, and Elliott Wave International’s Jeff Kennedy has written about five of them in a Trader’s Classroom column. For an example of why people are so fascinated by Fibonacci, read part of Kennedy’s article here:

* * * * *

How to Apply Fibonacci Math to Real-World Trading
Have you ever given an expensive toy to a small child and watched while the child had less fun playing with the toy than with the box that it came in? In fact, I can remember some of the boxes I played with as a child that became spaceships, time machines or vehicles to use on dinosaur safaris.

In many ways, Fibonacci math is just like the box kids enjoy playing with imaginatively for hours on end. It’s hard to imagine a wrong way to apply Fibonacci ratios or multiples to financial markets, and new ways are being tested every day. Let’s look at just some of the ways I apply Fibonacci math in my own analysis.

Fibonacci Retracements
Financial markets demonstrate an uncanny propensity to reverse at certain Fibonacci levels. The most common Fibonacci ratios I use to forecast retracements are .382, .500 and .618. On occasion, I find .236 and .786 useful, but I prefer to stick with the big three. You can imagine how helpful these can be: Knowing where a corrective move is likely to end often identifies high-probability trade setups (Figures 7-1 and 7-2).

figure 7-1

figure 7-2

Kennedy then goes on to explain Fibonacci extensions, circles, fans and time, using 11 charts to show what he means. Whether or not you are a math geek, you can learn a lot from this six-page introduction to Fibonacci math.

Get Your Fibonacci Techniques Right Here. Jeffrey Kennedy has been using and teaching these techniques for years, and he has written a quick description of five Fibonacci techniques in his Trader’s Classroom column — now available to you for free by signing up as a Club EWI member. Read more about the 6-page report here.

Elliott Wave International (EWI) is the worlds largest market forecasting firm. EWIs 20-plus analysts provide around-the-clock forecasts of every major market in the world via the internet and proprietary web systems like Reuters and Bloomberg. EWIs educational services include conferences, workshops, webinars, video tapes, special reports, books and one of the internets richest free content programs, Club EWI.