The Fibonacci sequence

 
The Fibonacci sequence has been named after Leonardo of Pisa also known as Fibonacci (a mix of the words Filius Bonacci, which means son of Bonacci). He first described this sequence in the year 1202 in his book Liber Abaci. Although he is seen as the first who discovered this sequence, It was later discovered that this sequence was already known by Indian mathematicians.

 

The Fibonacci sequence:

0, 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987 …

 
Each element in the sequence comes by adding the last two elements. For instance, the number 13 is achieved by adding the numbers 5 and 8 and the number 21 is achieved by adding 8 with 13. You might not help wondering why is the sequence so famous? What is Fibonacci? The explanation can be seen if the sequence is depicted visually since then it becomes clear that the sequences describes a growth pattern in nature. See the picture below which explains the fibonacci spiral.
 

 
The number 1 in the sequence stands for a square with each side 1 long. The number 2 stands for a square of 2 by 2 and so on. If the sides of the square are placed next to each other a new side of a larger square forms as explained before, e.g. 2+3 gives 5 and same goes for the squares. This can be repeated till infinity and with each step the squares get larger. Thing that is so special about this sequence can be seen when a line is drawn trough the cross points.
 

 
With these picture is becomes apparent what the sequence actually represents. This pattern is seen in many natural ophenomeneon, for example in a nautilus or even in the shape of a galaxy, but it doesn end here. The sequence also has a connection with the golden ratio.
 

Read about the life Fibonacci
Read about the occurrence of the Fibonacci sequence in Tool’s song Lateralus