Leonardo Fibonacci, born in the 12th century, was an Italian mathematician. He is known to have introduced the "Fibonacci numbers" into Medieval Europe. These are a sequence of numbers where each successive number is the sum of the two previous numbers. E.g. 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc. Therefore;
Starting with 1,
1 + 1 = 2
1 + 2 = 3
2 + 3 = 5
3 + 5 = 8
5 + 8 = 13
And so on. The most amazing thing is that each of these numbers is approximately 1.618 times the previous number. This means that dividing any two successive Fibonacci numbers yields 1.618 (144/89, 55/34 etc).
These Fibonacci sequences are phenomenally all around us and found in just about anything; human hand bones, shells, flower petals, bird colorations, human faces, pyramids, and the list goes on.
Technical analysts use many of the significant Fibonacci ratios as support and resistance levels; regularly markets reverse back to these key levels before continuing into the same direction. These levels are created by taking the ‘trend range’ – the distance between two extreme points (A & B) and then dividing the distance of the range by the key Fibonacci ratios of 23.6%, 38.2%, 50%, 61.8% and 100%.
It is amazing to see how often the market will reverse back and then stop dead on one of these levels before heading back into its original direction (or waver around in between these levels like a trading range).
Through back testing, traders can find markets with ‘fluctuation pull backs’ that have a high probability of retracing back into this price region, (between the 38.2% and the 61.8% Fibonacci levels), before heading back into its original direction. Using this, combined with a reversal candle pattern, a trader could trade the market out of this pull back as the market continues its upward trend. These could be powerful entry or re-entry signals used within their trading plan (like the hammer candle reversal we can spot on the bar chart between these levels below).
Fibonacci, Elliott Wave and Cycle analysis theories all provide very accurate turning points in the market and the ability for traders to gain early entry into newly formed trends; they also project forward potential ends to the new trend with an indication on when to exit the market.
 
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