The Golden Number
The Internet is teeming with information about the Golden Number.
Some of it is well-documented and serious, some esoteric, some completely fanciful.
Man has always tried to measure and quantify the world around him. To do so, he has used the measurements and proportions of his own body. Until the French revolution of 1789 (birth of the metric system), the whole world measured its environment in "palms", "palms", "empans", "feet" and "cubits".
These five measures have the following peculiarity: the sum of two adjacent measures equals the next measure (palm palm = empan; empan foot = cubit) and the ratio between two adjacent measures is constant, and equals the number 1.618: palm x 1.618 = palm, palm x 1.618 = empan, empan x 1.618 = foot and foot x 1.618 = cubit. The cubit, or "royal Egyptian cubit", was equivalent to 52.9 cm (after the reform under the XXVIth dynasty of the pharaohs).
Although Euclid (300 BC) already spoke of this ratio of two lengths in his "Elements", this proportion was called "divine proportion" by Luca Pacioli, a mathematician contemporary of Leonardo da Vinci (1509), and much later "Golden Section" by the German philosopher and mathematician Adolf Zeising around 1850, and finally "Golden Number" in 1932, by the Romanian diplomat Matila Ghyka.
Certainly first used in geometry, the Golden Number (named φ or "Phi" after the Greek architect of the Parthenon, Phydias) represents a constant ratio between two quantities of the same kind, such as lengths, surfaces, volumes or numbers. Phi is an irrational number, and is equal to (1 √5)/2 , an approximate value of 1.618.
To give a simple definition of the Golden Number, we could say that it represents the ratio between the length of a cubit and that of a foot. It is therefore part of the construction of the human body. This is undoubtedly what gives it its mystique.
Try an amusing and surprising experiment: measure the ratio between the first and second phalanges of one of your fingers, then the ratio between the third and second: you'll get a number close to 1.618.
The same goes for the ratio between your hand and your forearm. And if you divide your own height by 1.618, you get the height of your navel!
For hundreds, even thousands of years, the Golden Ratio has been used to define ideal proportions between two geometric or mathematical entities. It lies at the boundary between these two fields, and symbolizes their union.
It represents a kind of standard of proportion, and while it has been used (or detected) primarily in architecture and painting, it can also be found in fields as diverse as science, physics, nature, but also music or even finance or acoustics.
With the exception of the 19th century, it's almost certain that the Golden Number has been used deductively (i.e. consciously) throughout history, but there's virtually no written proof of this. Its deliberate use may nevertheless have remained a secret, passed down from generation to generation by certain trades such as architects, journeymen or the great painters: some have even called it "the Initiate's Number".
Today, the "Number" is no longer as secret as it once was. Nevertheless, it remains mythical and still retains a mystical and mysterious side for some.
Its conscious application in fields such as architecture, painting, sculpture, industrial aesthetics, craftsmanship, interior design, landscaping, marketing and many others is well established.
For many, the Golden Number represents the ultimate in harmonious proportions, and many of the buildings we see around us feature these ratios, while a large number of advertising logos are designed on this principle.
The result is that, whatever our opinion and level of knowledge about it, we live with it constantly, and have it consciously or unconsciously in front of our eyes at all times.
Returning to the structure of a painting, the Golden Number is not the only system that has been used.
This Wikipedia article will give you a fairly exhaustive overview of the composition systems that have been and are still in use.
Below you'll also find links to two well-documented American sites dealing with the art of composition and the Golden Ratio.
The process of adopting a structuring system is a reasoned choice. Experience shows that this approach takes nothing away from creativity and inspiration. Once the idea has been accepted, it saves you time, confidence and visual harmony in your field of expertise!
Let's quote Le Corbusier once again: "The regulating layout does not bring poetic or lyrical ideas; it does not inspire the theme; it is not creative; it is a balancer. A problem of pure plasticity".