that geometry, in all its forms, is the mathematical discipline that has contributed most to the visual arts, this book sets out to show the fruitfulness of their relationships throughout all eras.
Giuseppe Longo and Sara Longo, in their article “Infinity of God and Space of Men in Painting”, evoke the contribution of the geometric perspective to Renaissance painting. From the mid-14th Century, armed with this new tool, artist-theologians were able to organize the space of men and symbolize their finitude, in the face of God’s infinite act.
Another contribution of geometry to painting is highlighted by Jean-Pierre Crettez in his two articles on “internal geometry” – a concept created by the author to show how classical painters such as Leonardo da Vinci and Georges de La Tour used geometry (invisible but revealed through its structural mesh) to ensure the coherence and harmony of their pictorial space.
Since the early 20th Century, geometry has had a plurality of forms: non-Euclidean geometry, catastrophe theory, algorithmic geometry, fractal theory, etc. In her article “Geometry and the Life of Forms”, Ruth Scheps explains how these various geometric currents have inspired geometric abstract artists – from suprematism to digital art, via optical art, kinetic art, conceptual art and minimalism.
A special case of artistic inspiration, derived from geometric and natural forms, is provided by Giuseppe Longo and Sara Longo in their article “Among the Trees: Iterating Geneses of Forms, in Art and Nature”, which presents the fractal geometric structure as a source of inspiration for the “Komorebi” project (an untranslatable Japanese word that refers to the effect of sunlight through the foliage).
At the interface of art and science, or belonging to both, scientific drawings and photography have also given rise to artistic works, as illustrated by the article by Bruno Chanetz, “The Passion of Flight: from Leonardo da Vinci to Jean Letourneur”, and by Jean Letourneur himself, “Sculptor of Fluid Movement”, whose drawings and sculptures draw their inspiration from visualizations created by an engineer at ONERA.
Finally, the most contemporary tools for experimental visual art are, no doubt, provided by advances in computer modeling and simulation. Sophie Lavaud, in her article “Emergilience, an Art Research Project”, explains her project: exploring the conditions necessary for the emergence, through self-organization, of “infinite dynamic picture-systems” composed of collective and global shapes and phenomena.
Introduction written by Ruth SCHEPS and Marie-Christine MAUREL.
1 1 Bill, M. (1949). The mathematical way of thinking in the visual art of our time. Werk, 3.
2 2 Dali, S., Crucifixion (Corpus Hypercubus), oil on canvas, 194.3 x 123.8 cm, 1954. The Metropolitan Museum of Art, New York.
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