Difference between revisions of "Mathematics and art"

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Mathematics and art are related in a variety of ways, and have a long historical relationship.

Mathematics has itself been described as an art motivated by beauty.

Mathematics and the arts

Mathematics can be discerned in arts such as music, dance, painting, architecture, sculpture, and textiles.

Mathematics and visual arts

This article focuses on mathematics in the visual arts.

History

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.

Mathematics has directly influenced art with conceptual tools such as linear perspective, the 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 in engravings by M. C. Escher.

Computer art often makes use of fractals including the Mandelbrot set, and sometimes explores other mathematical objects such as cellular automata.

Controversially, the artist David Hockney has argued that artists from the Renaissance onwards made use of the camera lucida to draw precise representations of scenes; the architect Philip Steadman similarly argued that Vermeer used the camera obscura in his distinctively styled paintings.

Other relationships include the algorithmic analysis of artworks by X-ray fluorescence spectroscopy, and stimuli to mathematics research, especially Filippo Brunelleschi's theory of perspective which eventually led to Girard Desargues's projective geometry.

Sacred geometry

The belief that God created the universe according to a geometric plan has ancient origins.

A persistent view, based ultimately on the Pythagorean notion of harmony in music, holds that everything was arranged by Number, that God is the geometer of the world, and that therefore the world's geometry is sacred.

Plutarch attributed the belief to Plato, writing that "Plato said God geometrizes continually" (Convivialium disputationum, liber 8,2).

In modern times, the mathematician Carl Friedrich Gauss adapted this quote, saying "God arithmetizes".

William Blake's The Ancient of Days draws upon Pythagorean principles.

As late as Johannes Kepler (1571–1630), a belief in the geometric underpinnings of the cosmos persisted among some scientists.

See Sacred geometry.

See also

• Art
• Golden ratio
• List of mathematical artists
• Mathematical beauty
• Mathematical object
• Mathematics
• Recursion
• Sacred geometry
• Visual arts

External links

• Mathematics and art @ Wikipedia
• Sacred geometry @ Wikipedia