
Binarium
The Best Binary Options Broker 2020!
Perfect For Beginners and MiddleLeveled Traders!
Free Demo Account!
Free Trading Education!
Get Your SignUp Bonus Now!
Bloomberg
We’ve detected unusual activity from your computer network
To continue, please click the box below to let us know you’re not a robot.
Why did this happen?
Please make sure your browser supports JavaScript and cookies and that you are not blocking them from loading. For more information you can review our Terms of Service and Cookie Policy.
Need Help?
For inquiries related to this message please contact our support team and provide the reference ID below.
How Fibonacci numbers help in technical analysis?
a ltyd d XyxNN mYmkr b vn y XOGsB TaM R RGR a vBjBW g izWHS i Qdp n IdQfM g DWarZ e B AxIB u G l bO l Z , HXMwh vzsoa L xgPA L Kyv C cc
Let me answer your question in short and tothepoint manner.
Fibonacci numbers are basically numbers In a sequence where every number in it is the sum of the two preceding numbers.
Such as 1,1,2,3,5,8,13 and so on.
They appear everywhere in Nature, from the leaf arrangement in plants, to the pattern of the florets of a flower, the bracts of a pinecone, or the scales of a pineapple.
In technical analysis, these numbers represent ‘Retracement levels’ (points from where a particular trend will reverse). These levels are of much use to technical analysts since they represent entry and exit points.
Part 24: Technical Analysis – Fibonacci Sequence
GitHub is home to over 40 million developers working together to host and review code, manage projects, and build software together.
Clone with HTTPS
Use Git or checkout with SVN using the web URL.
Downloading
Want to be notified of new releases in Schachte/Fibonacci_Analysis ?
Launching GitHub Desktop
If nothing happens, download GitHub Desktop and try again.

Binarium
The Best Binary Options Broker 2020!
Perfect For Beginners and MiddleLeveled Traders!
Free Demo Account!
Free Trading Education!
Get Your SignUp Bonus Now!
Launching GitHub Desktop
If nothing happens, download GitHub Desktop and try again.
Launching Xcode
If nothing happens, download Xcode and try again.
Launching Visual Studio
Latest commit
Files
Permalink
Different methods of computing the fibonacci sequence using recursion, dynamic programming and matricies.
 Method 1: Basic recursive call. Not efficient because it recomputes already computed values in the recursion tree. Exponential time complexity .
 Method 2: Dynamic programming approach #1. Efficient in the sense of time because we use a table to compute future values. O(N) time complexity .
 Method 3: Dynamic programming approach #2. Efficient in the sense of time and good with space. O(N) time complexity .
 Method 4: QMatrix Approach. Very efficient. O(log(n))
 © 2020 GitHub, Inc.
 Terms
 Privacy
 Security
 Status
 Help
You can’t perform that action at this time.
You signed in with another tab or window. Reload to refresh your session. You signed out in another tab or window. Reload to refresh your session.
Fibonacci Sequence
The Fibonacci Sequence is the series of numbers:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, .
The next number is found by adding up the two numbers before it.
 The 2 is found by adding the two numbers before it (1+1)
 The 3 is found by adding the two numbers before it (1+2),
 And the 5 is (2+3),
 and so on!
Example: the next number in the sequence above is 21+34 = 55
It is that simple!
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, .
Can you figure out the next few numbers?
Makes A Spiral
When we make squares with those widths, we get a nice spiral:
Do you see how the squares fit neatly together?
For example 5 and 8 make 13, 8 and 13 make 21, and so on.
The Rule
The Fibonacci Sequence can be written as a “Rule” (see Sequences and Series).
First, the terms are numbered from 0 onwards like this:
Type  Name  Latest commit message  Commit time 

Failed to load latest commit information.  
n =  0  1  2  3  4  5  6  7  8  9  10  11  12  13  14  . 
x_{n} =  0  1  1  2  3  5  8  13  21  34  55  89  144  233  377  . 
So term number 6 is called x_{6} (which equals 8).
Example: the 8th term is
the 7th term plus the 6th term:
So we can write the rule:
Example: term 9 is calculated like this:
Golden Ratio
And here is a surprise. When we take any two successive (one after the other) Fibonacci Numbers, their ratio is very close to the Golden Ratio “φ” which is approximately 1.618034.
In fact, the bigger the pair of Fibonacci Numbers, the closer the approximation. Let us try a few:
Note: this also works when we pick two random whole numbers to begin the sequence, such as 192 and 16 (we get the sequence 192, 16, 208, 224, 432, 656, 1088, 1744, 2832, 4576, 7408, 11984, 19392, 31376, . ):
It takes longer to get good values, but it shows that not just the Fibonacci Sequence can do this!
Using The Golden Ratio to Calculate Fibonacci Numbers
And even more surprising is that we can calculate any Fibonacci Number using the Golden Ratio:
The answer always comes out as a whole number, exactly equal to the addition of the previous two terms.
When I used a calculator on this (only entering the Golden Ratio to 6 decimal places) I got the answer 8.00000033. A more accurate calculation would be closer to 8.
Try it for yourself!
You can also calculate a Fibonacci Number by multiplying the previous Fibonacci Number by the Golden Ratio and then rounding (works for numbers above 1):
Example: 8 × φ = 8 × 1.618034. = 12.94427. = 13 (rounded)
Some Interesting Things
Here is the Fibonacci sequence again:
n =  0  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  . 
x_{n} =  0  1  1  2  3  5  8  13  21  34  55  89  144  233  377  610  . 
There is an interesting pattern:
 Look at the number x_{3} = 2. Every 3rd number is a multiple of 2 (2, 8, 34, 144, 610, . )
 Look at the number x_{4} = 3. Every 4th number is a multiple of 3 (3, 21, 144, . )
 Look at the number x_{5} = 5. Every 5th number is a multiple of 5 (5, 55, 610, . )
And so on (every nth number is a multiple of x_{n}).
1/89 = 0.011235955056179775.
Notice the first few digits (0,1,1,2,3,5) are the Fibonacci sequence?
In a way they all are, except multiple digit numbers (13, 21, etc) overlap, like this:
0.0 
0.01 
0.001 
0.0002 
0.00003 
0.000005 
0.0000008 
0.00000013 
0.000000021 
. etc . 
0.011235955056179775. = 1/89 
Terms Below Zero
The sequence works below zero also, like this:
n =  .  6  5  4  3  2  1  0  1  2  3  4  5  6  . 
x_{n} =  .  8  5  3  2  1  1  0  1  1  2  3  5  8  . 
(Prove to yourself that each number is found by adding up the two numbers before it!)
In fact the sequence below zero has the same numbers as the sequence above zero, except they follow a ++ . pattern. It can be written like this:
Which says that term “n” is equal to (в€’1) n+1 times term “n”, and the value (в€’1) n+1 neatly makes the correct 1,1,1,1. pattern.
History
Fibonacci was not the first to know about the sequence, it was known in India hundreds of years before!
About Fibonacci The Man
His real name was Leonardo Pisano Bogollo, and he lived between 1170 and 1250 in Italy.
“Fibonacci” was his nickname, which roughly means “Son of Bonacci”.
As well as being famous for the Fibonacci Sequence, he helped spread HinduArabic Numerals (like our present numbers 0,1,2,3,4,5,6,7,8,9) through Europe in place of Roman Numerals (I, II, III, IV, V, etc). That has saved us all a lot of trouble! Thank you Leonardo.
Fibonacci Day
Fibonacci Day is November 23rd, as it has the digits “1, 1, 2, 3” which is part of the sequence. So next Nov 23 let everyone know!

Binarium
The Best Binary Options Broker 2020!
Perfect For Beginners and MiddleLeveled Traders!
Free Demo Account!
Free Trading Education!
Get Your SignUp Bonus Now!