The Golden ratio
The Internet is teeming with information about the Golden ratio.
Some are documented and serious, others esoteric, others completely whimsical.
Man has always tried to measure and quantify the world around him. For this, he used the measurements and proportions of his own body. Until the French Revolution of 1789 (the birth of the metric system), the whole world measured its environment in "palms", "hands", "spans", "feet" and "cubits".
These five measurement units have the following characteristic: the sum of two adjacent measurements is equivalent to the following measure (hand + palm = span, span + foot = cubit) and the ratio between two adjacent measurements is constant and equals 1.618: hand x 1.618 = palm, palm x 1.618 = span, span x 1.618 = foot and foot x 1.618 = cubit. The cubit, or "Egyptian royal cubit" was 52.9 cm long (after the reform under the XXVIth dynasty of the Pharaohs).
If Euclid (300 BC) already speaks of this relationship of two lengths in his "Elements", this proportion was called "divine proportion" by Luca Pacioli, a contemporary mathematician of Leonardo da Vinci (1509), and much later "Golden section" by the German philosopher and mathematician Adolf Zeising around 1850 and finally "Golden ratio" in 1932 by the Romanian diplomat Matila Ghyka.
Certainly used first in geometry, the Golden ratio, (referred to as φ or "Phi" in honor of the Greek architect of the Parthenon, Phydias) represents a constant relation between two magnitudes of the same nature, surfaces, volumes or numbers. Phi is an irrational number, and it is equal to (1 + √5) / 2, which the approximating value is 1.618.
To attempt to give a simple definition of the Golden ratio, we could say that it represents the ratio between the lenght of the cubit and the one of the foot. It is therefore part of the construction of the human body. This is doubtless what confers on him this mystical side.
Try an amusing and surprising experiment: measure the ratio between the first and second phalanxes of one of your fingers, then the ratio between the third and the second: you will get a number close to 1.618.
Same for the relationship 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 is at the border of these two areas, and symbolizes their meeting.
It represents a kind of proportional standard, and if it has been used (or has been detected) above all 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.
Except since the nineteenth century, it is almost certain that the Golden ratio has been used in history in a deductive (i.e. conscious) way, but virtually no writing proves it. Its deliberate use has nevertheless remained secret and passed on from generation to generation by certain tradespeople such as architects, companions or great painters: some even called it "the Number of the Initiate".
Today, the "Number" is no longer as secret as it has been in history. It remains nevertheless mythical and still retains a mystical and mysterious side for some.
Its conscious application in areas such as architecture, painting, sculpture, industrial aesthetics, crafts, interior decoration, landscaping, marketing and many other fields is no longer to be proved .
The Golden ratio representing for many the pinnacle of harmony in proportions, many buildings built around us feature these ratios, and a large number of advertising logos are designed on this principle.
The result is that whatever be our opinion and our level of knowledge about the Golden ratio, we live constantly with it, and we consciously or unconsciously see it on all occasions.
To go back to the structure of a picture, the Golden number is not the only system that has been used in the history of art.
This Wikipedia article, written in french, will give a fairly comprehensive overview of the composition systems that have been and are still being used.
Below are links to two well-researched American websites 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 does not detract from creativity and inspiration. Once the idea is accepted, it saves you a lot of time and visual harmony in your area of expertise !
Let us quote again this statement of Le Corbusier: "The regulating lines system does not bring poetic or lyrical ideas, it does not in any way inspire the theme, it is not a creator, it is a balancer; a problem of pure plasticity."