**Mathematics and art **
- Mathematics is the study of relationships using numbers -- their
operations, interrelations, combinations, generalizations, and
abstractions -- and of shapes,
forms, and spaces
-- their
structure, measurement,
transformations, and generalizations.
The science of numbers.
It uses signs, symbols,
and proofs, and includes arithmetic, algebra, calculus, geometry,
and trigonometry. Mathematics is also the performace of calculations
-- the calculations involved in a process,
estimate, or plan of action, using reason and usually a special
system of symbols and rules for
organizing them.

A study by the Arts Education Research Center at NYU has shown that achievement test scores in academic subjects improve when the arts are used to assist learning in mathematics, creative writing, and communication skills. This seems likely because so many concepts have interdisciplinary importance to both of these disciplines.

In order to appreciate how critical mathematics is in the study of visual art, consider the importance of regular and irregular shapes (the circle, ovals, and polygons for instance) and forms (sphere, polyhedrons, etc.), in being able to draw, paint, or sculpt them, sometimes one must use mathematical formulae and procedures to calculate or measure their dimensions, area, or volume. In order to cast a form in a metal, one must know the temperature of its melting point. One must understand proportions in order to represent nature without distortion.

In producing or understanding a line, it may be necessary to measure length, width (and maybe even thickness), angle in degrees,

"Mathematics" is a plural form but takes a singular verb.

Although in mathematics the word "figure" stands for a number, in art it stands for a person or object. [That's noteworthy, don't you think?!]

**Examples of art incorporating
applications of mathematics:**

Babylon,

Inscription Representing the Square Root of 2, 1st or 2nd millennium BCE, stone tablet, Yale U, Princeton, NJ. See inscription.

Paolo Uccello (born Paolo di Dono) (Italian,
1397-1475), *Perspective
Study of a Chalice*, pen
and ink on paper,
29 x 24.5 cm, Gabinetto dei Disegni, Uffizi, Florence. See linear perspective, Renaissance, and wireframe.

Albrecht Dürer (German, 1471-1528),

Melancholia 1, 1514, copper plate engraving, 25 x 19 cm. This picture is loaded with mathematical instruments and symbols as an angel broods over the nature of the universe.In the upper right of Dürer's engraving, just below a bell, he placed a "magic square." There are many versions of this mathematical puzzle. This one can be decoded as "1514," the year Dürer witnessed the appearance of a bright comet at the same moment that a deadly plague was sweeping across Europe; the year the artist produced this design. Here's a link to an explanation of how the magic square works.

Architect Charles E. Jeanneret, known as "Le Corbusier" (French, 1887-1965), often used golden rectangles in his designs for buildings. One of these is the United Nations building in New York. The dimensions of the upright part of the L has sides in a specific proportion called the Golden Mean or Golden Section -- a specific mathematical relationship of one side's length to the other -- and there are distinctive marks on this taller part which again divide the height of the building in a display of this special mathematical relationship. The Golden Mean produces a harmonic effect called eurythmy found in nature as well as in a wide variety of works of art and design. Artists of various periods and cultures have found that dimensions determined by this formula are aesthetically appealing. See architect.

Maurits Cornelis Escher (Dutch, 1898-1972),

Other World, 1947, color wood engraving and woodcut printed in black, red-brown, and green, printed from three blocks; image 12 1/2 x 10 1/4 inches (31.8 x 26.1 cm), sheet 39.2 x 32.9 cm; Fine Arts Museums of San Francisco, CA. Depending upon which of this room's three windows we look out, we find our point of view is completely different and irreconsilable from each of the others. See optical illusion.

S. Harris (American, contemporary),

American Scientist, c. 2000, pen and ink on paper. See cartoon.

- "Whoever despises the high wisdom
of mathematics nourishes himself on delusion and will never still
the sophistic sciences whose only product is an eternal uproar."

Leonardo da Vinci (1452-1519), Italian Renaissance artist, quoted by N. Rose, in*Mathematical Maxims and Minims*, Raleigh, NC, 1988. Leonardo was famously a many of diverse accomplishments. Along with his achievements in painting and sculpture, he did innovative his work in geometry and mechanics.

- "He who loves practice without theory
is like the sailor who boards ship without a rudder and compass
and never knows where he may cast."

Leonardo da Vinci (1452-1519), Italian Renaissance artist.

- "Life is painting a picture, not
doing a sum."

Oliver Wendell Holmes Jr. (1841-1935), American Supreme Court Justice from 1902-1932.

- "Math and Mona Lisa" was a program on American National Public Radio about the science of looking at art, with a focus on how Leonardo da Vinci used math to influence the way we see his most famous portrait.

Also see advocacy, accuracy, Afrocentrism, Bloom's Taxonomy, circumference, civilization, coefficient of expansion, computer graphics, diagram, diameter, digital image, digital photography, digitizing, dingbat, empirical, empiricism, equilateral, Golden Mean or Golden Section, graph, helix, linear perspective, multiple intelligence theory, numbered, numismatics, parabola, parallel, parameter, pattern, phenomenology, pi, radial and radial balance, research, science and art, sequence, standards, symmetry or symmetrical balance, technology, tessellation, theory, time, vertex, volute, and wavelength.

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