Sunday, September 10, 2006

Phi and Fibonacci Sequence.....................................

I was reading the novel of " The Da Vinci Code" when I was stroke by the fact of the golden number Phi = 1.618 and Fibonacci sequence and their relation to nature,music,art,.... How come I didn't know about this before?

Fibonacci sequence is the famous series : 1,2,3,5,8,13,... where each number is the sum of the two numbers before. Not only this ! the result of each number divided by the number that comes before is constant which is PHI=1.618.

What is Phi?

Phi ( = 1.618033988749895... ), is simply an irrational number like pi ( p = 3.14159265358979... ), but one with many unusual mathematical properties. Unlike pi, which is a transcendental number, phi is the solution to a quadratic equation.

Phi is considered as the Golden Number which natural ratios is based on. We can see this in Human body as illustrated by Leonardo Da Vinci in the famous painting of the Vitrovian Man ( Up there).To acheive this,Da Vinci had to study dead corpses after looking for them in graveyards or buy them...sometimes being genius requires some lunacy !

He found out that Phi number is the result of dividing the length of a human's leg to the distance between his knees to toes.This can also applied in many parts of the body like arms,fingers,face, is always Phi that divides the body into magical and constant proportions.

Phi can be also seen in animals and plants like Dolphins :

Spiral Growth of sea shells:

Phi can also be seen in DNA spirals :

Also,Certain solar system orbital periods are related to Phi like Mercury,Venus,Earth,Jupitar and Saturn.

The Phi number has been used also by the Egyptian in the design of the Pyramids.Greek started using it in their architecture for beauty and balance and artists in their paintings also for the same reason.

The last picture is for the Notre Dame in Paris.

Phi also exist in famous musical Symphonies like Bethoven's fifth Symphony.
It is also used for Population growth and Stock Market.
Phi also exists in Theology concerning the creation of God and some symbols in the holy books.

God,everything in this universe goes in an amazing harmony.It is never random...never !!