Le Nombre D'or on Windows Pc

The number of gold (or golden section, golden ratio, or divine proportion) is a proportion, initially defined in geometry as the unique ratio a / b between two lengths a and b such as the ratio of the sum a + b of the two lengths on the largest (a) is equal to that of the largest (a) on the smallest (b) that is to say when:

{\ displaystyle {\ frac {a + b} {a}} = {\ frac {a} {b}}
The division of a segment into two lengths satisfying this property is called by Euclid division in "extreme and average reason". The golden number is now often referred to as φ (phi).

This irrational number is the only positive solution of the equation x2 = x + 1. It is worth:

{\ displaystyle {\ frac {1 + {\ sqrt {5}}} {2}} \ approx 1 {,} 6180339887} a.
He is involved in the construction of the regular pentagon. Its algebraic properties link it following Fibonacci and the quadratic body ℚ (√5). The number of gold is also observed in nature (some phyllotaxies, for example in sunflower capitules, Penrose tiling of quasi-crystals) or in some works and monuments (architecture of Le Corbusier, music of Xenakis, painting of Dalí).

The story of this proportion begins at a period of antiquity which is not known with certainty; the first known mention of division in extreme and average reason appears in the Elements of Euclid. In the Renaissance, Luca Pacioli, an Italian Franciscan monk, puts it in the spotlight in a textbook of mathematics and calls it "divine proportion" by associating it with an ideal sent from heaven. This vision develops and is enriched by an aesthetic dimension, mainly during the nineteenth and twentieth centuries when the terms "golden section" and "golden number" are born.

It is erected in aesthetic theory and justified by arguments of a mystical order, as an important or even explanatory key in the comprehension of the structures of the physical world, particularly for the criteria of beauty and especially of harmony; his presence is then claimed in the sciences of nature and life, proportions of the human body or in the arts such as painting, architecture or music. Some artists, such as the composer Xenakis or the poet Paul Valéry have adhered to part of this vision, supported by popular books. Through science, archeology or the sciences of nature and life, science invalidates theories of this nature because they are based on abusive generalizations and inaccurate assumptions.


The Golden ratio
● The continuation of Fibonacci
● Link
● Art
● Nature
● Mathematics
● Balance sheet

Geometry
Proportion
Rectangle and gold spiral
Pentagon and pentagram
Trigonometry
Arithmetic
Continuous fraction
Diophantine equation
Whole ℚ (√5)
Fragments of history
antiquity
Middle Ages
Renaissance
birth of a myth
the paroxysm
Nature
Presence
phyllotaxis
Human body
Work of the man
Painting
Archeology
Architecture
Music
Mathematical aesthetics
Notes and references
Notes
References
Attachments
Related articles
Bibliography
external links

Le nombre d'or φ
1.0v

Allows applications to open network sockets.
Allows applications to access information about Wi-Fi networks.
Allows an application to read from external storage.
Allows applications to access information about networks.