(except from USING MATHEMATICAL STRUCTURES TO GENERATE ARTISTIC DESIGNS)

Reprinted with permission from Mathematics Teacher, copyright May 1974, by the National Council of Teachers of Mathematics. All rights reserved.

By SONIA FORSETH

University of South Florida

St. Petersburg, Florida

and

ANDRIA PRICE TROUTMAN

University of South Florida

Tampa, Florida

THERE is a close relationship between mathernatics and art. The mathematician, with all the vigor of the artist, uses creative means to define and explore new mathematical structures. The artist searches for dynamic structures on which to base new images. Both explore the many facets of an idea in order to discover unique or unusual patterns and relationships. Therefore, it is not unreasonable for the artist to use mathematical structures, which in themselves display intrinsic beauty, as a basis for generating interesting designs.

Throughout history various cultures have exhibited examples Of this unique marriage between mathematics and visual arts. The Greeks used the "golden mean" as a structure of perfection in their architectural designs and sculpture. The Moors generated intricate symmetrical patterns in their mosques, and during the Renaissance, artists such as Da Vinci, Michelangelo, and Titian used mathematical structures as a source of order for their great works of art.

The traditional syrnbols used in mathematics such as 0, 8, x, y, or A2 are changed to symbols the artist uses; namely, color, line, texture, shape, and composition. By changing traditional mathematical symbols to those the artist uses, a technique is developed that can become a stimulating classroom activity. This technique can challenge the student's ability to use mathematical structures competently and can foster his creative abilities.

These designs may be constructed on plain or grid paper with magic markers, crayons, construction paper, or paint.

May 1974