Use this tag for questions related to art and mathematics, the applications of mathematics in art, or vice versa.
Mathematics and art are related in a variety of ways. Mathematics can be discerned in music, dance, painting, architecture, sculpture, and textiles but has its strongest relationship with visual arts.
Artists have used mathematics since at least the 4th century BC when Greek sculptor Polykleitos wrote his Canon, prescribing proportions based on the ratio $1:\sqrt2$ for the ideal male nude. Persistent popular claims have been made for the use of the golden ratio in ancient art and architecture. In the Italian Renaissance, Luca Pacioli wrote the influential treatise De Divina Proportione (1509), illustrated with woodcuts by Leonardo da Vinci, on the use of the golden ratio in art. Another Italian painter, Piero della Francesca, developed Euclid's ideas on perspective in treatises such as De Prospectiva Pingendi and in his paintings. Engraver Albrecht Dürer referred often to mathematics in his work Melencolia I. In modern times, graphic artist M. C. Escher used tessellations and hyperbolic geometry, with the help of mathematician H. S. M. Coxeter, while the De Stijl movement, led by Theo van Doesburg and Piet Mondrian, explicitly embraced geometrical forms. Mathematics has inspired textile arts such as quilting, knitting, cross-stitch, crochet, embroidery, weaving, Turkish and other carpet-making, as well as kilim. In Islamic art, symmetries are evident in forms as varied as Persian girih and Moroccan zellige tilework, Mughal jali pierced stone screens, and muqarnas vaulting.
Mathematics has directly influenced art with conceptual tools such as linear perspective, analysis of symmetry, and mathematical objects such as polyhedra and the Möbius strip. Magnus Wenninger creates colorful stellated polyhedra, originally as models for teaching. Mathematical concepts such as recursion and logical paradox can be seen in paintings by Rene Magritte and engravings by M. C. Escher. Computer art often makes use of fractals such as the Mandelbrot set and other mathematical objects such as cellular automata.
