0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 ...
Each number is a sum of the previous two:
1=1+0, 2=1+1, 3=1+2, 5=2+3 ...
The Fibonacci sequence is named after Leonardo of Pisa - nickname of Fibonacci.
The higher up in the sequence, the closer two consecutive "Fibonacci numbers" of the sequence divided by each other will approach the golden ratio (approximately 1 : 1.618 or 0.618 : 1).
Fibonacci was the first mathematician who introduces Hindu-Arabic numerological system in Europe, primarily through the publication in the early 13th century of his Book of Calculation, the Liber Abaci.
Fibonacci sequence is not so important as the quotient of the adjacent terms that possesses an amazing proportion, roughly 1.618, or its inverse 0.618. This proportion is known by many names: the golden ratio, the golden mean, PHI and the divine proportion, etc. So, why is this number so important? Well, almost everything has dimensional properties that adhere to the ratio of 1.618, so it seems to have a fundamental function for the building blocks of nature.
The Great Pyramid of Giza built around 2560 BC is one of the earliest examples of the use of the golden ratio. The length of each side of the base is 756 feet, and the height is 481 feet. So, we can find that the ratio of the vase to height is 756/481=1.5717.. The Rhind Papyrus of about 1650 BC includes the solution to some problems about pyramids, but it does not mention anything about the golden ratio Phi.
Raising interest to Fibonacci numbers today is connected to its use on stock market figures. Fibonacci numbers are commonly used in Technical Analysis with or without a knowledge of Elliot wave analysis to determine potential support, resistance, and price objectives. 38.2% retracements usually imply that the prior trend will continue, 61.8% retracements imply a new trend is establishing itself. A 50% retracement implies indecision. 38.2% retracements are considered natural retracements in a healthy trend.
If we go way back in time, we'll find that all numbers are associated with Arabic, Egyptian alphabet,and of course, symbols that represent planets. Originally, planetary system used the symbols of nine planets and all our numbers derived from it. First representation of idea of universal (astronomic) order has been illustrated by Tree Of Life.