The fibonacci sequence is a series of numbers in which each number is the sum of the two preceding ones. e.g. 0, 1, 1, 2, 3, 5, 8, 13, 21, 34. Start at 1, add the previous number (0) and get 1. Then, 1+1=2, 1+2=3, 2+3=5, etc.
Here is a visual representation of the fibonacci sequence drawn out as squares:
Each square, starting from the center, have side lengths corresponding to the fibonacci sequence. Note that the two previous squares have a side length equal to the proceeding square.
We can draw an arc through each square to create a spiral:
This spiral is known as the Fibonacci spiral. It is closely related to the golden spiral, which grows by a factor of Phi (φ) every quarter turn.
The pattern and proportions of the golden spiral are often found in nature. For example, seashells and flowers. Phi is an irrational number, approximately equal to 1.618... It is also called the golden ratio.
As the numbers increase in the sequence, the ratio between the numbers gets closer to Phi. For example, 13/8 = 1.625... 21/13 = 1.615... and 34/21 = 1.619... So, the Fibbonacci spiral is an approximation of the golden spiral.
Sequence: