The golden ratio: from the discovery of mathematicians to the aesthetics of Instagram

The golden ratio, also called divine proportion, dictates a harmonious relationship between the different parts of an object or an image.

The mathematician Étienne Ghys, in an article in World recalls that:

“When we decompose an object into two unequal parts, we say that the proportion is divine, or golden, if the ratio between the large part and the small is the same as the ratio between the whole and the large part. "

It is represented by the number φ phi (fi) and has a direct link with the name of the Greek sculptor Phidias at the origin of the facade of the Parthenon of Athens. Its value is 1,61803398874989482045… the result of a mathematical equation known since ancient Greece, namely (1 + √5) / 2.

Is good the mathematical language which is at the origin of aesthetic notions such as proportion, harmony or the principle of symmetry. According to the mathematician Hermann Weyl: "all the a priori results of physics have their origin in symmetry".

Beauty and goodness

From Antiquity therefore, the aesthetic virtues attributed to the golden ratio are multiple and tend to quickly exceed the harmony and balance of the spatial organization. They are thus largely transposed to the inner balance of being and souls. Also, for Aristotle, the beautiful is necessarily harmonious and proportionate ; for Socrates and Plato, a beautiful body can only be the reflection of a beautiful soul. This Hellenist equation keeps a very strong imprint in our civilization: remember the fairy tales in which all the princes and princesses are beautiful and beautiful; the good guys are beautiful and the bad guys much less.

The Italian mathematician Leonardo Pisano, known as Fibonacci, born in 1175, succeeded in developing a sequence, commonly known as the Fibonacci sequence. It is based on dividing one term by the previous one, each new result approaching more and more… the golden ratio. Tom Hanks, in Da Vinci Code, tries to decode a message on a crime scene: it is none other than this Fibonacci sequence. The architecture of the Louvre pyramid, inspired by the Egyptian pyramids, is based on proportions close to those defined by the golden ratio.

Define the beautiful

Through mathematics, the arts, the sciences or philosophy, all civilizations have tried to define the beautiful. In antiquity, various theorists of sculpture pre-established canons of beauty from this idea of ​​just proportions, of a harmonious whole. The so-called Polycletus cannon thus defended that a beautiful body should be equal to seven times the height of the head. Until the Renaissance, beauty was only a mimesis of nature, organized and structured by the balance of the golden ratio. This “divine” proportion helped to reproduce the divine creation by copying its balance. Therefore, the canons of beauty translate a new vision of man, more anthropomorphic.

Leonardo da Vinci applied the divine proportion to theVitruvian man, a kind of ideal man, giving form to the theory according to which nature and therefore the body of man is the very example of the balance of proportions. The navel being the central point of the human body as well as of the square in which it is integrated. This application of the golden ratio in Greece and Rome until the Renaissance reflects an idealization of the beautiful - echoed by Leonardo da Vinci, Boticcelli and even Michelangelo.

The Vitruvian Man, by Leonardo da Vinci.



Vitruvius, Roman architect who lived in the Ier century BC AD, considered that:

“For a building to be beautiful, it has to have the perfect symmetry and proportions like those found in nature. "

Many artists were inspired by the multiple geometric models offered by nature to achieve works of harmonious proportions and this is still the case in contemporary times. In the middle of the XXe century, art, architecture, nature and mathematics still intersect in Corbusier's system of measurement: the Modulator.

Nature was also the greatest source of inspiration for the Catalan architect Gaudí. Think of the columns like trees inside the Sagrada Familia or even the Barcelona paving marked with the helix of the snails. Gaudí's art nouveau fascinates art and architecture schools, but also fashion (see the Max Azria fall / winter 2015-2016 collection) and will also be the subject an exhibition event at the Musée d'Orsay in 2022.

Gaudi paving, in Barcelona.



The influence of social networks

If since antiquity, the balance of forms has guided a number of creations at the origin of what is called the "fine arts", XNUMXst century media are not left out and have been able to integrate these codes. From the golden ratio to the rule of thirds.) in photography as in cinema there is only one step. Instagrammers have understood the interest of an aesthetically balanced and neat photography thanks to the golden ratio and isn't the Instagram feed (the personal portfolio of each user) a juxtaposition of three columns allowing everyone associations of images and poetic ideas on the canvas?

Heirs to a long history of images, we tend to reproduce them instinctively or like the most familiar proportions. The @instarepeat account proves it: the weight of certain photos has made them standards not only because they invite you to travel, to poetry, but also because they send us back to a "comfortable" aesthetic experience. for our eye accustomed to certain proportions. The users of the networks put themselves in scene with the same objective in photographs which certainly dictate and reflect criteria of beauty, but through the more or less conscious reproduction of lines of flight or of proportions able to retain the attention, they too are under the influence of the golden ratio.

On the @insta_repeat account.



The balance of the body and of the artistic compositions is a reflection of constantly evolving social values, as is the perception of beauty from one era to another. By abuse of language, to speak of the golden ratio or to claim its use amounts simply to speaking of the beautiful or the sense of harmony. Many mathematicians deny the interest of this number and stress that certain shapes or objects considered fairly universally as harmonious do not at all fall within this proportion. In the recent history of the hard sciences, the golden ratio seems to arouse little interest.

On the contrary, it continues to fascinate and inspire artists, like a myth or a mystical notion. There is something fascinating about the name itself, like a magical and mysterious key that would make it possible to create beauty. The golden ratio fascinates because it is a kind of knot where a mathematical concept and aesthetic transpositions intermingle in very varied fields, attesting to its mythical aura which is unlikely to lose ground in another era. more concerned with the image and aesthetics.

The author of this article dedicates it to the students of Master 2, International Trilingual Management, Spanish-speaking markets (2021-2022) of the University of Paris-Est Créteil who enriched the course "Art, advertising and marketing: study of case of the Spanish-speaking market ”.

Sabrina grillo, Lecturer in the civilization of contemporary Spain, Paris-Est Créteil Val de Marne University (UPEC)

This article is republished from The Conversation under Creative Commons license. Read theoriginal article.

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