There is a ‘magical’ number, or ratio, that keeps recurring in nature that some people have said indicates a divine pattern or structure to the universe.

It’s called the Fibonacci sequence, after the Italian Leonardo Fibonacci who wrote about it in the early 13^{th} century – although the pattern had been observed by Indian mathematicians as early as the 6^{th} century.

If you’re wondering what this has got to do with finance, read on. This same ‘golden ratio’, as it is also called, seems to occur in stockmarket movements, too.

The mathematical sequence starts 1,2,3,5,8,13,21,34,55 and continues *ad infinitum*, with each number being the product of the two preceding numbers.

### Golden mean

That’s not the clever bit, however. What is startling is the ratio between numbers in the series, which is always either, roughly, 1.618 or 0.618, depending on whether you are going up or down the sequence.

The Fibonacci ratio is found by dividing one number in the series by the number that precedes it – so for example, 21÷13=1.61; 55÷34=1.61.

If you reverse the process, and divide a number in the series by the one that follows it, you arrive at a ratio of 0.61 in every case – so for example, 34÷55=0.61.

In percentage terms, that’s 61.8%, which has become known as the ‘golden ratio’ or ‘golden mean’.

In mathematics it’s known as *phi* (not to be confused with *pi, *the numerical value of the ratio of the circumference of a circle to its diameter).

A further key Fibonacci ratio is derived by dividing one number in the series by the number two places to the right, producing a ratio of 38.2% – so 13÷34=38.2%.

Yet another ratio is found by dividing one number in the series by the number that is three places to the right – for example 8÷34=0.2352 or 23.6%.

### Golden rectangle

This same ratio, *phi,* produces the ‘golden rectangle’ – a rectangle where the ratio of the sides equals the golden mean of 1.61. These golden rectangles can then be nested within each infinitely by rotating each successive rectangle through 90º to form what is known as a logarithmic spiral.

So, for example, if you had a rectangle that was 21cm long by 13cm wide, if you placed another rectangle 13x8cm at right angles, within the original, you could then place another 8x5cm rectangle at 90º within that, and so on down the scale.

Here are some astonishing examples from nature.

The vast majority of flower petals follow the Fibonacci sequence – the lily has three petals, buttercups five, delphiniums eight, corn marigold 13, chicory 21, the daisy 34.

### Spiral galaxies

If you divide the number of female bees by the number of male bees in a hive it produces the ratio 1.61.

Human features seem to follow the golden mean – the nose and mouth are positioned between the eyes and the bottom of the chin according to the ratio, and it has often been said that faces considered the most attractive are those that conform most closely to *phi*.

The ratio of the uterus in a human female, length to width, is 1.6, when she is at her most fertile age.

The nautilus shell follows the same logarithmic pattern in the golden rectangle – as do spiral galaxies in Space. The Milky Way has several arms, like a Catherine Wheel, each with a logarithmic spiral of roughly 12º.

DNA, too, follows the Fibonacci sequence. Each molecule is 34 angstroms long by 21 angstroms wide – both numbers in the Fibonacci series – and their ratio is…1.61.

### Fibonacci retracements

There are many, many more examples. But what has this to do with trading?

Well, as I hinted earlier, stockmarket fluctuations seem to frequently follow Fibonacci patterns.

They are known as Fibonacci retracements, because when you are looking at a graph of the movement of a particular stock, those lines keep tracing back to the same golden ratios – representing areas of either support for a falling stock or resistance to a rising stock.

Six lines are drawn on a chart. The first at the highest point a stock has reached over a given time period, representing 100%, the second at 61.8%, the third at 50% (not a Fibonacci number) the fourth at 38.2%, the fifth at 23.6% and the final one, 0%, at the lowest point of price movement.

As the price of the stock fluctuates, you will frequently find resistance or support at these levels. In short, whichever way the price is moving, it often reverses at these points.

### Fibonacci Arcs and Fans

You can also use these ratios to create Fibonacci Arcs, drawing circular arcs radiating downwards from the 100% mark at 38.2%, 50% and 61.8%, like rings on a target, which will indicate the probable range of price movement.

Fibonacci Fans follow the same principle: a vertical line is drawn at the right-hand edge of the graph and divided into the same percentages, and lines drawn across the graph from the bottom left-hand corner, starting at a given time period, to meet those percentage marks. The resulting lines will show areas of probable support and resistance.

Many trading platforms have automated graphing systems that allow you to create your own Fibonacci traces for your chosen stock over a set time period.

It’s probably not a good idea to use this as your only means of trading, but tapping into the design of the universe and combining this knowledge with other factors could just help boost your winning percentages.