WEEK 8 

Reflection on

Dancing Mathematics and the Mathematics of Dance 

by Sarah Marie Belcastro and Karl Schaffer

In this journal article, the authors, who are both into math and dance, explain how math is connected to dance. They point out that counting steps and noticing shapes in dance involve math, and deeper connections exist where math inspires and solves dance problems. They share their experiences in modern dance and other styles, showing how math is present in the rhythm and patterns of movements. They discuss how different dance traditions, like ballet and Bharatya Natyam, use math in their unique ways, such as creating lines and symmetry. The authors explore how symmetries in dance can interact with each other. They focus on four specific symmetries: translation, mirror reflection, 180-degree rotation, and glide reflection. By combining these symmetries in pairs, they create what's known as the Klein four group or Z2 ⊕Z2. They illustrate this concept using three dancers, showing that a mirror reflection of the first dancer leads to the position of the second dancer, a 180-degree rotation of the second dancer corresponds to the third dancer, and this is equivalent to applying a glide reflection to the first dancer. The authors note that similar outcomes occur when combining any pair of symmetries from the original list, always resulting in one of the four symmetries mentioned.

The authors share how they've blended math and dance in various performances. Karl and Erik Stern's show combines math discussions with dances exploring basketball physics and tap dance rhythms. Sarah-marie's ballet trio, "Crystalline Meringue," uses symmetries, while "Swirly Suite I" incorporates binomial coefficients. Karl, Scott Kim, and Barbara Susco's "Trio for Six" involves finger geometry and illusions.

                                                        

 Karl's recent dance, "Fragments," explores war's fragmentation using tangram pieces, leading to a math question about polyhedra. The article also discusses the influence of mathematical patterns on rhythm in dance.

dance by Dr Schaffer and Mr stern

Stop 1

"Each dance tradition has its own characteristic way of using mathematical concepts. For example, classical Western ballet and Bharatya Natyam both use a strong sense of line. However, as Karl’s teacher Kathryn Kunhiramen pointed out to him, in Bharata Natyam the dancer’s lines end—they are cut off by abstract or representational mudras made by flexing the hands. This situates the dancer “in the world,” rather than extending beyond it into the “world of the gods.” In contrast, the ballet dancer’s lines extend toward infinity, symbolizing an endless extension over the natural world."(p.16)

Ballet

Bharatanatyam

This paragraph is really interesting to me because it talks about how different dance styles use the idea of lines in unique ways. For instance, in Bharata Natyam, the lines created by dancers end with hand gestures, keeping them connected to the real world. In contrast, in classical ballet, a dancer's lines extend endlessly, suggesting a connection to the infinite and the natural world. As a math teacher and reader, it's cool to see how these dance styles express mathematical ideas in their own cultural and artistic ways. It's a reminder that math isn't just numbers; it can be found in various forms of art and expression.

Stop 2

The second stop is about the Klein group which I mentioned above. When we integrate math into art forms these types of abstract concepts can be easily understood by students. As a math teacher, this integration of group theory with dance not only makes the subject more engaging but also emphasizes the broader applicability of mathematical concepts beyond traditional problem-solving contexts. It encourages students to see mathematics as a dynamic and creative tool that can be used to understand and appreciate various forms of art and expression.

Question

How can educators effectively integrate mathematical concepts, with dance in higher grade levels to foster a deeper appreciation for both disciplines and enhance students' analytical and creative skills? Do you have any experience in this?

Reference

Belcastro, S. M., & Schaffer, K. (2011). Dancing Mathematics and the Mathematics of Dance. Math Horizons, 18(3), 16-20. Taylor & Francis, Ltd. on behalf of the Mathematical Association of America. https://doi.org/10.4169/194762111X12954578042939