The Golden Number

This number, the number of harmony and beauty, can be calculated with many ways. Here are some of them :

An equation : the golden number is the positive solution of the equation x²-x-1=0. It exact value is (square root of 5 + 1)/2, so it's about 1.618.
A continued fraction : the value of this fraction is equal to the golden number : 1+1/(1+1/(1+1/(1+ ...)))
The Fibonacci sequence : a number in this sequence is the addition of the two previous numbers. It can be illustrated by the drawing below. We find the golden number when we divide a number of the sequence by it's previous. Bigger the number is, more the result is precise.

The golden number can be found in the everyday-life. For example, we can found it :

In pine cone : Where we found the Fibonacci sequence. Here there are 8 green lines and 13 red lines, which are two consecutive numbers of the sequence.
In the human body : First, with arms. If you divide the length of an arm by the one of the hand, you find an approximate value of the golden number. Next, studies were done, particularly by Leonardo da Vinci, who create the "Vitruvian Man". We take "a" the length between the belly button and the chest, and "b" the one between the chest and the top of the forehead. If we divide "b" by "a", we find an approximate value of the golden number.

We can find the golden number in lots of paintings, like :

In the Mona Lisa : Where we can find a spiral which each side is built by fractions which contains the golden number : 1/Phi, 1/Phi², 1/Phi^3, ...
In the Birth Of Venus : Which have the proportion of a golden rectangle.

We can find the golden number in lots of architectures. The most famous are :

The Parthenon : it contains golden rectangles, which are rectangles where the division of their length by their width is equal to the golden number. We find it again in the United Nations Headquarters.
The Kheops Pyramid : in this pyramid; "a" is equal to 612 foot and "s" equals 378 foot : if you divide "a" by "s", you find about 1.619, so approximately the golden number.