The Golden Ratio and Fibonacci

The Golden Ratio or Mean is a mathematical proportion that appears everywhere in nature. This proportion divides a line into two unequal segments, where the proportion of the whole line to the larger segment is equal to the proportion of the larger segment to the smaller segment. When we value the whole line as 1, then the Golden Ratio is 0,61803.
From time immemorial this proportion is regarded to be the ultimate proportion of perfection, harmony and sometimes even divinity. From arts to architecture to music one can recognise the Golden Ratio. Examples of this are the Notre Dame in Paris, the great pyramids of Egypt and even musical pieces by Mozart. But also in nature the Golden Ratio occurs. Our body, face, heartbeat and handwriting consist of this proportion, up until cellular level. The Golden Ratio is to be found in every human being – no matter how tall or short – in the navel. Even the courses of the stock exchange and the Hebrew alphabet hold the Golden Ratio.
Fibonacci
The famous Fibonacci numbers form the initial principle to the Golden Ratio. This string is formed by constantly adding the previous two numbers, which results in the following eternal string: 1,1,2,3,5,8,13,21,34,55 … etc. The proportion between all following numbers is approximately the Golden Ratio. This proportion appears regularly in the geometrical shapes of the universe, for example the leafs on trees and plants, the arrangement of sunflower seeds and the Nautilus shell spiral.
 
 
 
Golden Ratio & Fibonacci [du]
Golden Ratio in Art & Architecture [eng]
Sacred Geometry and Golden Ratio [eng]