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Mathematics and art are related in a variety of ways. Mathematics has itself been described as an art motivated by beauty. Mathematics can be discerned in arts such as music, dance, painting, architecture, sculpture, and textiles. This article focuses, however, on mathematics in the visual arts.
Mathematics and art have a long historical relationship. Artists have used mathematics since the 5th century BC when the Greek sculptor Polykleitos wrote his Canon, prescribing proportions based on the ratio 1:√2 for the ideal male nude. Persistent popular claims have been made for the use of the golden ratio in ancient art and architecture, without reliable evidence. 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. The engraver Albrecht Dürer made many references to mathematics in his work Melencolia I. In modern times, the graphic artist M. C. Escher made intensive use of tessellation and hyperbolic geometry, with the help of the mathematician H. S. M. Coxeter, while the De Stijl movement led by Theo van Doesberg 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 jaali pierced stone screens, and widespread muqarnas vaulting.
Illustration of an artist using a camera obscura. 17th century
Proportion: Leonardo's Vitruvian Man, c. 1490
Hotamis kilim (detail), central Anatolia, early 19th century
The complex geometry and tilings of the muqarnas vaulting in the Sheikh Lotfollah Mosque, Isfahan
Architect's plan of a muqarnas quarter vault. Topkapı Scroll
Mathematical sculpture by Bathsheba Grossman, 2007
Fractal sculpture: 3D Fraktal 03/H/dd by , 2003
Fibonacci word: detail of artwork by Samuel Monnier, 2009
God the geometer. Codex Vindobonensis, c. 1220
William Blake's The Ancient of Days, 1794
Dalí's Crucifixion (Corpus Hypercubus), 1954, with the net of a hypercube
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