Introduction to Fibonacci
Fibonacci Series
Fibonacci series has become famous in math because of its inherent advantages in accurately estimating modelling problems. In space, geography, nature, art, music, and even finance. An Italian mathematician introduced an exponential sequence of numbers that each number is the sum of the preceding two numbers:
0, 1,1, 2, 3, 5, 8, 13, 21…
0+1=1
1+1=2
2+1=3
2+3=5
3+5=8
5+8=13
8+13=21
21+34=55
…
Here is a longer list:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, …
The mathematical relation between numbers made it easy to understand and simple to continue. The proportion of numbers revealed a more practical edge in a way that Fibonacci ratios multiply the functionality many times.
Fibonacci Ratios
Fibonacci series has amazing properties which will be uncovered until calculating the proportion of numbers. From deep inside of Fibonacci series, the "Golden Ratio" was born. It's a number that's equal to approximately 1.618 and is simply calculated by constantly dividing one number ahead into the just previous one:
- 8/5 = 1.6
- 13/8 = 1.625
- 21/13 = 1.615
- 34/21 = 1.61
- …
This chain continues with different assumptions and reaches various numbers. By dividing the lower number into the next higher number, the answer will be 0.618:
- 34/55 = 0.618
- 89/144 = 0.618
- 144/233 = 0.168
- ...
The next Fibonacci ratio is 0.318. Simply calculated by dividing one number into the next two one, For example, 55 into 144.
- 55/144 = 0.318
- 144/377 = 0.318
- 377/ 987 = 0.318
- ...
By going one step higher and dividing each number into three next number, 0.236, another important Fibonacci ratio is extracted.
- 89/377 = 0.236
- ...
To wrap up,
Fibonacci ratios are 23.6%, 38.2%, 61.8%. Obviously, key ratios like 0%, 50% and 100% can be there too.
Application of Fibonacci Ratio in Technical Analysis
Fibonacci is one of the practical tools in technical analysis. In many cases, Fibonacci represents a reliable forecast of the market and lots of traders put into work and do business on that. Corresponding to Fibonacci ratio, one level is drawn and in many cases, they overlap with strong static trendlines like support and resistance. Technical analysis applies the ratio of Fibonacci series for retracement and extension in price action.
Fibonacci retracement (RT) is looking for the following retracement possible levels that trend may reach in the return direction. The start point is equivalent 0% level and the endpoint is where it becomes 100%.
Fibonacci extension, on the other hand, indicates the possible growing area in following the previous level. Factors like chart patterns play the main role in this part.