What is Fibonacci? – Part 1

The Fibonacci Sequence, one of the most well-known formulas in mathematics, was invented by the Italian Leonardo Pisano Bigollo (or Leonardo Fibonacci) in his book “Liber Abaci”.

Simply put, each number in the sequence is the sum of the two numbers that precede it. For example: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144… To infinity.

This sequence was then found to create what is known as the “golden spiral” which implements these numbers into a “golden rectangle”. Each square is a Fibonacci number timesed by itself (8×8, 13×13 etc).

To get the Fibonacci spiral, draw a line starting in the bottom corner of a golden rectangle within the first square (start of the blue line) and then touch each succeeding multiple squares outside corners, this creates a Fibonacci spiral that continues forever.

Fibonacci Golden Spiral

Fibonacci sequence is seen in many things of nature so here is a smaller list of examples: Fibonacci can be found in sunflowers, korus, snails, eggs, many vegetables like romanesque broccoli & spiralled chillis. In pinecones, chameleon tails, waves, shells, whirlpools, spiral galaxies, and may even be visible in your own fingerprints.

Examples of Fibonacci in Nature

The Fibonacci sequence is all about proportion, and the 1.618 ratios (or its inverse 0.618) is referred to as the “golden ratio” or the “golden mean ratio”. This ratio is essential in almost everything and you can find it throughout nature. 

In the Fibonacci sequence, every number is approximately 1.618 times greater than the previous number. You can multiply one number by 1.618 and it will give you approximately the next number in the sequence.

Calculating numbers in the Fibonacci Sequence:

  • 3 x 1.1618 = (5)
  • 5 x 1.618 = (8)
  • 8 x 1.618 = 12.944 (13)
  • 13 x 1.618 = 21.034 (21)
  • 21 x 1.618 = 33.978 (34)
  • 34 x 1.618 = 55.012 (55)

To add to the importance of the golden ratio, here is another example.
If you take any two successive numbers in the sequence and divide them, their ratio gets closer to 1.618 as you go further along in the sequence:

3/2 = 1.5
8/5 = 1.6
13/8 = 1.625
21/13 = 1.6153
34/21 = 1.61904
… 196418/121393 = 1.61803

In the next part, I will show how you can implement Fibonacci into your technical analysis.

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  • Zahir says:

    Great job with explaining the basics and importance of Fibonacci. Waiting for the next parts in the series.

  • $tan13 says:

    Thank you Olley, very interesting subject and the way you explain everything is easy to understand. Why I didn’t have maths school teacher like you . Could have liked maths probably…😉

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