A brief departure, because these 2 posts, at the beginning at least, are more about arithmetic than forex trading – it’s the basis of Fibonacci retracement, taken right from first principles, and hopefully as simply as possible at every step

For all those that want it – and even if you think you don’t want to know, it might just worth checking out….

Let’s start with the so-called Fibonacci sequence, or Fibonacci numbers

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610….

The first number of the sequence is 0, the second is 1, and each following number in the sequence is equal to the sum of the previous two numbers.

Leonardo of Pisa, nicknamed Fibonacci, published all this in 1202 – but most of the basic ideas were around since classical Greece and Rome – where it had a lot to do with architecture.

It’s a ‘natural’ pattern – draw a set of squares, with sides 1, 1/2, 1/3, 1/5, 1/8 etc and then draw the quarter of the circle that cuts their diagonal corners and you end up with this.

You get a nice spiral shape – actually a helix, a flat spiral (spirals are spirals because you could wind them round a church spire, top to bottom).

Let’s take 2 adjacent terms in the series, and divide them

233/144 = 1.61806
377/233 = 1.61803

As you go higher up the series, the result of dividing 2 adjacent terms gets closer and closer to an irrational constant, φ = 1.6180 approximately.

This is known as the golden mean or the golden ratio – so how far off are the successive quotients on the series – how inaccurate are they as an approximation…?

φ – 1/1 = +0.618
φ – 2/1 = -0.382
φ – 3/2 = +0.118
φ – 5/3 = -0.0486
φ – 8/5 = +0.0180

These are the ‘magic’ numbers that will be reappearing when it comes to drawing Fibonacci retracement lines on an actual forex chart – which is for the next post….

One Response to “The Fibonacci Sequence”

1. The Fibonacci Sequence says:

   October 21, 2008 at 3:49 pm

   [...] Original post by ForexPerform [...]

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