Title: Seminole Patchwork
Grade Level: Elementary/Secondary
Topic: reflection, rotation, translation, and glide reflection
Description: A Web site which applies the concepts to Seminole patchwork. It is a model that might be translated for some beadwork patterns too.
Summary: (from website) Mathematicians have teamed up with archaeologists and anthropologists to investigate patterns and designs from around the world. By dividing the patterns into groups, these scientists can study the patterns unique to a culture and gain insight into a group’s cultural identity and whether nearby groups influenced each other’s work. They have found that people from very early times used highly sophisticated symmetry. Clearly mathematics did not begin in Greece in 500 BC. The Egyptians used patterns with complicated symmetries a thousand years earlier, and people all over the world could recognize the symmetries their own culture accepted, and those they did not.
The study of crystals led to most of the mathematical information we have on the symmetry of repeated patterns. In 1891, E.S. Federov completed a list of the 230 three-dimensional repeated patterns. In 1944, Edith Muller first used the 17 classes of two-dimensional repeated patterns in an analysis of material culture when she studied the Islamic art of the Alhambra in Spain. Through her pioneering work in 1944, she identified 11 of the 17 classes, and it was not until 1987 that mathematicians were able to document all 17 in the incredibly beautiful artistry achieved by the builders of the Alhambra. In 1948, Ann O. Shepard used symmetry analysis in the study of designs from the American Southwest, the Anasazi, Mimbres, and Rio Grande Pueblos. This important work is only now being fully appreciated.
Mathematicians, cognitive scientists, and anthropologists are working together to unravel the mysteries of the patterns. This study of symmetries from around the world may be able to provide us with a deeper understanding and appreciation of our human heritage.- Kay Gilliland, EQUALS