# Mathematics and Art Mathematics Is Term Paper

#### Excerpt from Term Paper :

Technology and art have been married in a number of ways, showing how the two may complement one another:

Mathematics provides a framework for artistic expression while art can awaken mathematical intuition, revealing aspects of mathematics that are otherwise hidden within abstract formulations (Cipra 748).

The marriage of technology and art has engendered considerable interest in academic circles, and among the recent developments have been a meeting of more than one hundred mathematicians, artists, and educators in 1992 to consider the trend among artists to visualize mathematical concepts. Artists have helped visualize difficult mathematical processes, and one that has been cited is the act of turning a sphere inside out without introducing a sharp crease at any point during the operation. This was demonstrated using computer graphics in 1989 after the procedure itself was described mathematically in 1959. The process is known as sphere eversion and has been pictured graphically by Francois Apery of the University of Upper Alsace in France (Peterson 299).

Another use of computers for creating art involves the use and creation of fractals, a geometry developed to study chaos theory, a geometry that focuses on broken, uneven, and wrinkled shapes (Briggs 22). Fractals are only one means of utilizing computer graphics in art, and the artistic expression possible with the computer has barely been tapped as yet. The growing awareness of links between math and art may produce new art forms in the coming years.

Various mathematical ideas and tools are used directly in graphic design. Mathematical grids are often used in the design of the printed page or some graphics for other purposes, with the grid laying out horizontal and vertical elements in a pleasing and orderly fashion. Graphic artists can use grids to create templates which can be used again and again for different design issues.

Artists have always studied nature and developed rules concerning design and proportion in order to create works as close to life as possible. Artists have also discerned certain mathematical principles that have becoming guides for their work, such as the ratio known as the Golden Mean. This is a mathematical atio of the larger side of a rectangle compared to the shorter. The ancient Greeks saw this as a ratio like pi, with both being irrational numbers. The Greeks used the Golden Mean in architectural design, and artists have used it in the construction of their paintings for centuries since. The ratio was thought by the Greeks to produce buildings that would be the most pleasing to the eye, and its use in painting often explains the way the artist balances different lines and masses in the frame. The Golden Mean is often used in other types of design as well and for the same reason, because it is believed to produce the most pleasing effect.

Both symmetry and asymmetry are also used in design. Symmetry can be based on translation, rotation, or reflection. Translation refers to the movement of a design in a linear direction so that the design is repeated again and again. Rotation turns the design around and reproduces it in different directions. Reflection reproduces the design as if in a mirror, often repeating the design in both a horizontal and vertical direction. Variations in the design can create asymmetry within the symmetry and may be used to give variation to the design and so to maintain interest.

Many more complex mathematical concepts are often translated into design elements, such as Fibonacci numbers, a numbering system found in nature in a wide variety of places and now used as part of the generator for fractals and other graphic designs on computer. The Fibonacci sequence shows each succeeding numb er in the sequence to be the sum of the two preceding numbers, as in the sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89. And so on. The pattern appears so often in the natural world that it is seen as one of the laws of nature, and artists make use of this principle in recreating images from nature and also in generating new designs in more abstract design forms.

Certain geometric forms are used in design because they are seen as natural and perfect, with some gaining spiritual significance as well. The mandala is such a design and appears in religious art and religious symbolism from various parts of the world, showing that many cultures have turned to nature and the idea of perfection for inspiration. The Mandela may also be called the sacred circle, with the circle seen as a perfect form found throughout nature. The kaleidoscope is a generator of Mandela designs, as can be a computer. Images of the circle adored with repeated graphic elements generated according to the principles of symmetry can be found throughout the world.

As noted, the design forms of the graphic arts from graphic design to computer design are most readily seen by the untrained eye as having a mathematical basis, though mathematics has also been a key element in representational painting and drawing through the ages as well. Artists have observed nature and discovered many of the same principles mathematicians have discovered, then applying those principles to their work.

Works Cited

Briggs, John. Fractals: The Patterns of Chaos. New York: Touchstone, 1992.

Chilvers, Ian, Harold Osborne, and Dennis Farr. The Oxford Dictionary of Art. New York: Oxford University Press, 1994.

Cipra, Barry. "Cross-Disciplinary Artists Know Good Math When They See it... " Science (7 Aug 1992), 748-749.

De La Croix, Horst, Richard G. Tansey, and Diane Kirkpatrick. Gardner's Art Through the Ages. New York: Harcourt Brace Jovanovich, 1991.

Fineberg, Jonathan. Art Since 1940. Englewood Cliffs, New Jersey: Prentice-Hall, 1995.

Goodman, Cynthia. Digital Visions: Computers and Art. New York: Harry N. Abrams, 1987.

Janson, H.W. History of Art. New York: Harry N. Abrams, 1969.…

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