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Math in Art

Shape Up!
Lakota people, United States <br><i>Dress</i>, 1880-90<br>Leather, cotton, copper disks, bells, glass beads<br>Minneapolis Institute of Arts<br>Gift of James David and John David
zoom Lakota people, United States
Dress, 1880-90
Leather, cotton, copper disks, bells, glass beads
Minneapolis Institute of Arts
Gift of James David and John David


Artists sometimes simplify forms that they see in nature, or in their imagination, into geometric shapes. These abstract shapes may then serve as symbols for the objects or geographical features that inspired them.

The Lakota of the Northern Plains often put abstracted geometric designs of animals, tipis, and their surroundings into the beadwork decoration on their clothing. This dress, which was worn during ceremonies, is embellished with various geometric shapes—triangles, squares, diamonds, circles. In Lakota culture, it was customary for women artists to use geometric symbols, whereas men worked in a more pictorial style.

Each shape and color on this dress symbolizes part of the Lakota creation story. The green U that falls over the wearer’s heart represents a turtle. A sacred animal to the Lakota, the turtle was the only creature able to bring mud up from the ocean floor so the Creator could mold the Earth and humans. Because of the turtle’s connection to creation and fertility, green U shapes and ovals are often seen on the yokes of women’s clothing. On this dress, the broad areas of blue stretching across the top are thought to signify the sky and a lake, separated by a tan line marking the shore. The large designs made up of diamonds and triangles could stand for stars, spiritual beings, clouds, or tipis, which are reflected in the lake. The cross-shaped designs in the lower blue band may represent the four directions. Every design, no matter how simple, symbolizes something spiritually important in the creation story.

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1. Modigliani’s sculptures and paintings of women rarely resemble the person he was portraying. He simplified this woman’s appearance, carving only her oval eyes, triangular nose, and circular mouth.
Amedeo Modigliani, Head of a Woman, 1911, limestone, Minneapolis Institute of Arts, gift of Mr. and Mrs. John Cowles
2. Much of Sol LeWitt’s art consists of instructions that are bought by a collector or a museum. People then follow the directions to create a drawing for a wall. Here, lines and angles added together form the composition. LeWitt leaves interpretation to the viewer.
Sol LeWitt, Wall Drawing #9 A & B, 1969/1996, graphite, colored pencil, Walker Art Center, gift of the artist
3. One of the best-known types of abstract art is Cubism. Speaking of his own work, the cubist painter Lyonel Feininger said, “What one sees must be transformed in the mind and crystallized.” Feininger reduced this painting’s subject to geometric shapes, but you can still tell what it is.
Lyonel Feininger, Gross-Kromsdorf I, 1915, oil on canvas, Minneapolis Institute of Arts, bequest of Putnam Dana MacMillan


March 2010