As you all know, this famous mathematical sequence draws a pattern that can be found everywhere in nature. In this short article, I'll assume that you know this sequence because I want to show you quickly 2, 3 -not so well known- properties about this sequence.

I - The fibonacci sequence and 'Phi' aka the Golden ratio

This sequence is often associated with "Phi" the golden ratio (1.618). But to be more precise the Fibonacci numbers are hovering around Phi. The ratio of successive numbers never reaches the golden ratio, but it comes closer to it toward the infinite. For example: - 1/1 is smaller than Phi - 2/1 is bigger than Phi - 3/2 is smaller than Phi (but closer) - 5/3 is bigger than Phi (but closer) and so on...

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II - The Fibonacci sequence and Vortex Math

Vortex Math is a quite particular and controversial mathematical field proposed by Marco Rodin & Randy Powell. They propose another way to perform the four basic operations (addition, subtraction, multiplication, division). If you want to know more feel free to take a look at the video below.

 In our situation, what you have to know is that basically Vortex Math is about reducing every numbers by adding its digits together until you get a number between 1 and 9. If you apply this operation to each number of the Fibonacci sequence you'll notice few interesting things. Indeed within this sequence, there is another hidden sequence that repeats itself to infinity. To see this, let's take the 24 first numbers (except 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 

If you add each digit of each number together, you get this result:

1 - 1 - 2 - 3 - 5 - 8 - 4 - 3 - 7 - 1 - 8 - 9 - 8 - 8 - 7 - 6 - 4 - 1 - 5 - 6 - 2 - 8 - 1 - 9

Now if we take the 24 following numbers:

75025 - 121393 - 196418 - 317811 - 514229 - 832040 - 1346269 - 2178309 - 3524578 - 5702887 - 9227465 - 14930352 - 24157817 - 39088169 - 63245986 - 102334155 - 165580141 - 267914296 - 433494437 - 701408733 - 1134903170 - 1836311903 - 2971215073 - 4807526976

We get the exact same sequence!

1 - 1 - 2 - 3 - 5 - 8 - 4 - 3 - 7 - 1 - 8 - 9 - 8 - 8 - 7 - 6 - 4 - 1 - 5 - 6 - 2 - 8 - 1 - 9

This 24 digits sequence will loop infinitely within the Fibonacci sequence!

III - The Fibonacci sequence and the number 9

Finally, this sequence is 'symmetrical '. Indeed, if we add the first number with the 13th, the second with the 14th and so on, we'll get constantly the number 9.

1 - 1 - 2 - 3 - 5 - 8 - 4 - 3 - 7 - 1 - 8 - 9
8 - 8 - 7 - 6 - 4 - 1 - 5 - 6 - 2 - 8 - 1 - 9
- - - - - - - - - - - - - - - - - - - - - - - - - - -
9 - 9 - 9 - 9 - 9 - 9 - 9 - 9 - 9 - 9 - 9 - 9

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