the golden ratio

I) introduction

since antiquity , artists and philosophers had belived to the existence about a propotion who allow to get harmony and beauty. the golden number is a raport which used in many estates as architecture , maths or in the natur. with the golden ratio you can build , paint ,sculpt and enrich your work with hided shape .

II)His value

Definition

the golden ratio is designate by the grec lettre phi , . the ratio "phi" in tribute to the great Phidias, who used the proportion frequently in his sculpture.

The golden number isn't a measure , or dimension , it' s a rapport between two homogeneous greatness.

It can be defined as that number which is equal to its own reciprocal plus one . the golden ration is equal to

for find the golden ration you take a golden section

after , you say that :

and clearing denominators gives and clearing denominators gives and clearing denominators gives

Using the quadratic equation and taking the positive sign , you find

Using the
The golden ratio is an irrational number and her handwriting is infinite

III)His history

Its history

We presume that the golden number appeared for the first time during the prehistory, when men learned to devise a circle in 5 parts.
Greek people owe its rigour, but some of its attributes were discovered long before. Indeed, the golden number appears in work or monuments antecedent to Greek antiquity, such as Egypt pyramids.
Euclide defined it the first in a written treaty: Les elements in the 3rd century. Research studies on this number were improved specially with Fibonacci and his succession.

But this number was not named yet. In 1509, Luca Pacioli published a book called La Divine Proportion, while Léornard de Vinci was spoken about “golden section” (“section aurea”). In the 18th century, the German Kepler qualified it as “jewel of geometry”.