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**The Fibonacci series are a mathematical sequence in which any number is the sum of the two preceding****numbers. The sequence goes as follows: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and so on. The properties of****this sequence appear throughout nature and also in the arts and sciences. Most notably the ratio of 1.618,****the “Golden Mean”, is very common, a relationship already discovered in ancient times. This number can****be approached by dividing a Fibonacci number by its preceding number as the sequence extends into****infinity. Besides, ratios of .618, which is the inverse of 1.618 are very prominent when analysing Fibonacci****relationships.****Elliott didn’t discover the Fibonacci relationships himself, but this was brought to Elliotts attention by****Charles Collins.****The wave counts of the impulsive and corrective patterns (5 + 3 = 8 total) are Fibonacci numbers, and****breaking down wave patterns into their respective sub waves produces Fibonacci numbers indefinitely.**

**Analysing Fibonacci relationships between price movements is very important for several reasons.****First you can control your wave analysis. The better the Fibonacci ratios of your wave count, the more****accurate your count is, because in some way or the other, all waves are related to each other. Secondly****you can project realistic targets once you have defined the wave count correctly or you have distinguished****different scenarios, which point in the same direction.****Since Fibonacci ratios manifest themselves in the proportions of one wave to another, waves are often****related to each other by the ratios of 2.618, 1.618, 1, 0.618, 0.382 and 0.236. This fact can help you in****estimating price targets for expected waves.**

**If, for example a wave 1 or A of any degree (or time frame) has been completed, you can project****retracements of 0.382, 0.50 and 0.618 for wave 2 or B, which will give you your targets. Most of the time****the third wave is the strongest, so often you will find that wave 3 is approximately 1.618 times wave 1.****Wave 4 normally shows a retracement, which is less than wave 2, like 0.236 or 0.382. If wave three is the****longest wave, the relationship between wave 5 and three often is 0.618. Also wave 5 equals wave 1 most****of the time.****The same relations can be found between A and C waves. Normally C equals A or is 1.618 times the****length of A.****You could even combine waves to find support and resistance zones. For example the net price****movement of wave 1 and 3 times 0.618 creates another interesting target for wave 5.****It is worthwhile to experiment a lot with your wave count, Fibonacci will help you to solve the rhythm of the****markets.**

**Targets for wave 1**

**The first wave, a new impulsive price movement, tends to stop at the base of the previous correction,****which normally is the B wave. This often coincides with a 38.2% or a 61.8% retracement of the previous****correction.**

**Targets for wave 2**

**Wave 2 retraces at least 38.2% but mostly 61.8% or more of wave 1. It often stops at sub wave 4 and****more often at sub wave 2 of previous wave 1. A retracement of more than 76% is highly suspicious,****although it doesn’t break any rules yet.**

**Targets for wave 3**

**Wave 3 is at least equal to wave 1, except for a Triangle. If wave 3 is the longest wave it will tend to be****161% of wave 1 or even 261%.**

# Targets for wave 4

**Wave 4 retraces at least 23% of wave 3 but more often reaches a 38.2% retracement. It normally reaches****the territory of sub wave 4 of the previous 3rd wave.****In very strong markets wave 4 should only retrace 14% of wave 3.**

**Targets for wave 5**

**Wave 5 normally is equal to wave 1, or travels a distance of 61.8% of the length of wave 1. It could also****have the same relationships to wave 3 or it could travel 61.8% of the net length of wave 1 and 3 together.****If wave 5 is the extended wave it mostly will be 161.8% of wave 3 or 161.8% of the net length of wave 1****and 3 together.**

**Targets for wave A**

**After a Triangle in a fifth wave, wave A retraces to wave 2 of the Triangle of previous wave 5. When wave****A is part of a Triangle, B or 4 it often retraces 38.2% of the complete previous 5 wave (so not only the fifth****of the fifth) into the territory of the previous 4th wave. In a Zigzag it often retraces 61.8% of the fifth wave.**

**Targets for wave B**

**In a Zigzag, wave B mostly retraces 38.2% or 61.8% of wave A. In a Flat, it is approximately equal to wave****A. In an Expanded Flat, it usually will travel a distance of 138.2% of wave A.**

# Targets for wave C

**Wave C has a length of at least 61.8% of wave A. It could be shorter in which case it normally is a failure,****which foretells an acceleration in the opposite direction.****Generally wave C is equal to wave A or travels a distance of 161.8% of wave A.****Wave C often reaches 161.8% of the length of wave A in an Expanded Flat.****In a contracting Triangle wave C often is 61.8% of wave A.**

**Targets for wave D**

**In a contracting Triangle wave D often travels 61.8% of wave B.**

**Targets for wave E**

**In a contracting Triangle wave E often travels 61.8% of wave C. It cannot be longer than wave C!**

**Targets for wave X**

**Wave X minimally retraces 38.2% of the previous A-B-C correction; a retracement of 61.8% is also****common.**