*Macmillan Science Library: Mathematics*. Copyright © 2001-2006 by Macmillan Reference USA, an imprint of the Gale Group. All rights reserved.

This section contains 261 words(approx. 1 page at 300 words per page) |

## Mathematics in Art

Escher's art is of particular interest to mathematicians because, although he received no mathematical training beyond his early years, he used a variety of mathematical principles in unique and fascinating ways. Escher's artwork encompasses two broad areas: the geometry of space, and the so-called "logic" of space.

On a visit to the Alhambra in Spain, Escher was inspired by the colorful geometrical patterns of tiles. He began to explore the various ways of filling two-dimensional space with symmetrically repeated arrangements of images known as tessellations. In the process, he discovered the same principles that had been developed previously, unknown to Escher, within the branch of mathematics known as group theory. When mathematicians and scientists became aware of his work, they helped popularize his art, and he soon gained an international reputation.

Subsequent interactions with mathematicians introduced Escher to other mathematical concepts that he explored in his art. Among the results are his so-called impossible constructions that appear reasonable but prove to be impossible to construct in three-dimensional space. He also employed **non-Euclidean geometry**, representations of infinite space, and various aspects of **topology**.

Although Escher completed his final graphic work in 1969, the popularity of his images continues today. Several Internet sites are dedicated to providing information about Escher and selling renditions of his art.

## See Also

Dimensions; Euclid and His Contributions; Mathematics, Impossible; Tessellations; Topology.

## Bibliography

Escher, M. C. *The Graphic Work of M. C. Escher.* New York: Meredith Press, 1967.

MacGillavry, Caroline H. *Symmetry Aspects of M. C. Escher's Periodic Drawings.* Utrecht: A. Oosthoek's Uitgeversmaatschappij NV, 1965.

This section contains 261 words(approx. 1 page at 300 words per page) |