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Banah Graf arranged turtle shapes
into repetitive patterns in this regular tessellation.

The Weave of the World:
What's Dance Got To Do With Math?   Just About Everything.

Reiner and Lang introduced students to the masterworks of the Dutch graphic artist Maurits Cornelis Escher and the American dance company Pilobolus, based in rural Connecticut but known to audiences worldwide. These artists create geometric patterns in highly innovative and dynamic ways. Students examined Escher's precise and fantastic worlds, delighting his engravings of morphing triangles, lizard mosaics, and staircases that trick the eye. They were intrigued by the ways in which the artist plays with natural phenomena -gravity, optics, and spatial dimensions.

They watched on videotape how Pilobolus undertakes similar explorations in dance. The leotard-clad dancers create geometric shapes and patterns with their bodies, joining hands and feet, or entwining in improbable clusters of torsos and appendages, only to metamorphose into new forms and patterns.

Early in the project, students completed worksheets on lines of symmetry and practiced arranging polygons into regular and semiregular tessellations. They drew their own tessellations by combining polygons into imaginative and colorful images-such as goldfish, foxes, and sunbursts-and arranging them into repetitive patterns. When Goodman, an accomplished professional dancer and seasoned instructor at Buckman Elementary in Portland, agreed to collaborate with Lang and Reiner on their project, he sat in on several classroom activities to familiarize himself with the concepts students were learning. He then began meeting with students in the school's auditorium.

Goodman captured the students' attention and imagination, and they worked with high energy and focus. He taught them to choreograph movement tessellations-brief dances or drill routines that combine the geometric principles students had been studying in the classroom. The auditorium echoed with young voices quickly mastering and mingling the two vocabularies of dance and mathematics.

"The arts are an integral part of mathematics, especially in the field of geometry," says Reiner. "If you don't relate mathematics to the real world, to such things as dance, you're doing a disservice to students. There is so much that you can get out of studying the arts that will help you to understand mathematics, it's incredible."

Lang agrees: "By bringing in the arts, students see that mathematics is not just present when they're sitting in their chairs in the classroom. It's all around-schools of fish, patterns in the sky, the flow of traffic. It all has a mathematical pattern."     more...