belcastro, s.-m., & Schaffer, K. (2011). Dancing mathematics and the mathematics of dance. Math Horizons, 18(3), 16–20. https://www.jstor.org/stable/10.4169/194762111x12954578042939
Introduction
In Dancing Mathematics and the Mathematics of Dance, belcastro and Schaffer explore the deep and often surprising connections between mathematical ideas and artistic dance. Although dance may appear purely expressive, the authors argue that mathematical structures are “intrinsic to dance,” appearing in rhythm, symmetry, spatial patterns, and choreographic design. They describe how dancers naturally use counting, geometric lines, and repeated patterns, while choreographers rely on transformations such as reflection, rotation, and translation to shape movement phrases. The article highlights both local symmetries within a single dancer’s body and global symmetries among groups of dancers.
The authors also discuss the influence of Rudolf Laban, whose movement theories use polyhedra to classify direction, effort, and spatial intention. For example, Laban mapped eight movement qualities—such as press, glide, flick, and punch—to the vertices of a cube. This blending of geometry and kinesthetic experience illustrates how mathematical models can guide artistic expression.
Beyond theory, belcastro and Schaffer describe their own mathematically inspired choreographic works. These include dances based on group theory, graph theory, rhythmic star polygons, and even game theory. One example involves dancers embodying the internal angles of a triangle to demonstrate that they sum to 180∘. Their creative process often moves fluidly between mathematics inspiring dance and dance inspiring new mathematical questions.
Ultimately, the authors emphasize that dance is multifaceted—artistic, social, expressive—and mathematics is just one lens through which it can be explored. Yet the interplay between the two fields enriches both, offering new ways to understand movement, structure, and creativity.
Reflection
Reading Dancing Mathematics and the Mathematics of Dance opened up an unexpectedly rich way of thinking about movement, beauty, and mathematical structure. What struck me most were the concrete dancing examples the authors used to reveal patterns that, on the surface, seem purely artistic but are deeply mathematical. The symmetry exercises, the hop step jump patterns, and especially the permutation based choreography immediately resonated with me. When I saw the composition table of symmetries, I was surprised by how similar it was to the examples I’ve shown my own students when teaching permutations and combinations. I had never considered that a dancer switching positions or reversing a phrase could be viewed as a permutation in motion. That realization made me rethink how dance can serve as a living, breathing model for mathematical ideas.
This connection feels like an exciting opportunity for the classroom. Integrating dance based patterns into lessons could help students see that mathematics is not confined to numbers on a page—it is a language that describes structure, rhythm, and form in the world around them. Using movement as an example might spark curiosity and help students appreciate mathematics as a kind of art, one that underlies many artistic traditions they already enjoy.
What deepened my appreciation even further was the authors’ thoughtful discussion of the relationship between mathematics and art. They write, “To be clear, we don’t view dance entirely through the lens of mathematics—or vice versa… Dance is many things, sometimes all at the same time” (p. 20). This perspective is powerful because it acknowledges that while mathematics can illuminate dance, it should not overshadow the emotional, cultural, and expressive dimensions that make dance meaningful. Instead, the goal is interdisciplinary dialogue—using math to analyze art and using art to reinterpret math.
This idea pushes me to think more broadly about what we are really doing when we bring mathematics into conversations about dance, music, or other creative fields. We are not trying to claim that math is the foundation of everything, even if mathematically inclined people sometimes feel that way. Rather, we are opening doors between disciplines that are too often kept separate. When students see math interacting with art, they gain a new lens through which to understand both. They may begin to view mathematical symbols not as abstract obstacles but as tools for describing patterns they already appreciate intuitively.
Ultimately, this interdisciplinary approach can help redefine what it means to be a “mathematician.” If math is allowed to be expressive, embodied, rhythmic, and creative, then more students may feel welcomed into the field. By showing that mathematics connects to the arts they love, we can cultivate a more inclusive and positive mathematical identity—one that invites curiosity rather than fear.
Question
What opportunities do you see for using dance, music, or visual art to help students understand abstract mathematical ideas?
Hi Lee,
ReplyDeleteThank you so much for the summary and reflection.I like your question because, honestly, I’m still in the early stages of exploring these relationships in my own teaching. As I read through the article and the activities that we did in our class, I couldn’t help but feel a little inspired, but also a little challenged, because, although I’m inspired by the possibilities, I also know that I haven’t used dance, music, or visual arts as much as I could in my math classes.
Most of my teaching has followed somewhat traditional models, based upon my own experiences of learning mathematics. However, now, I can see how many opportunities I may be passing up. Students already use rhythm, movement, pattern, and visual arts in their everyday lives. These things, in and of themselves, are mathematical.
I can imagine myself wanting to try more of these things. For example, using movement to explore transformations, rhythm to explore sequences, or visual arts to explore symmetry.
What this article has sparked in me is less “I already do that” and more “I want to try that.” The difference is that my thinking has shifted from seeing arts-based approaches as “creative” additions to seeing them as mathematical.
I'm also interested in hearing about how these ideas have been implemented in practice.
Hi Lee, I really enjoyed reading this. I liked how you explained the math in dance without making it feel like dance is being reduced to numbers. Your examples of symmetry and transformation made it easy to picture how dancers are constantly working with structure, even if they aren’t naming it as math.
ReplyDeleteReading this also made me think about Indian classical dance forms like Bharatanatyam and Kathak. So much of the movement is built on counting cycles, repeated rhythmic patterns, symmetry between the left and right side of the body, and precise spatial positions. The footwork especially feels very mathematical, with clear patterns, timing, and structure, but it’s always experienced as expression and storytelling first.
I also connected with what you said about permutations. In group dances, even small shifts in position or direction completely change how a sequence looks, which feels very similar to how we talk about permutations in math. It made me think about how powerful it could be for students to see these ideas happening through movement rather than only through symbols on paper.
I appreciated that you highlighted the authors’ point that dance is many things at once. Math can be one lens, but it shouldn’t override the cultural, emotional, and historical meanings of dance. For me, thinking about Indian dance really reinforces that idea.
Your question got me thinking about how movement-based traditions students already know could be a strong entry point into abstract math ideas. It feels like a way to make math more connected and inclusive.