Mathematics and Art

The connection between mathematics and art goes back thousands of years. The ancient Greeks and Romans used mathematics in sculptures and to aesthetically design buildings. In the 15th century Leonardo da Vinci wrote "Let no one read me who is not a mathematician." In the 16th century Durer employed mathematics to introduce perspective in drawings. In the 18th and 19th centuries mathematics was extensively used in the design of Gothic cathedrals, Rose windows, mosaics and tilings. In the 20th century geometric forms were fundamental to the cubists and many abstract expressionists. In recent decades several award winning sculptors have used topology as the basis for their pieces. The close connection between mathematics and art is most readily seen in the works of the Dutch artist M. C. Escher. Among the mathematical ideas represented in his work are: infinity, Möbius bands, tessellations, deformations, reflections, Platonic solids, spirals, symmetry, and the hyperbolic plane.

This fish design can be interpreted as a repeating pattern in the Poincare circle model of hyperbolic geometry. It is based on the regular tessellation {10,3} and fish like those in M. C. Escher's print Circle Limit III.

April is Mathematics Awareness Month. Each year the mathematics community celebrates the importance of mathematics in our lives. The theme for 2003 was "Mathematics and Art".