Mathematics of Maypole Dancing

Written by: Dr. Christine von Renesse.

This Fall (2016) the 13 students in my honors mathematical explorations class embarked on the journey of understanding some mathematical ideas behind maypole dancing. I say "some" because after several weeks of hard work we still have many open questions. We started by dancing around a pole (as you can see in the video below) and then shared what we were all curious about. While some questions addressed technical aspects of the dance (size of pole, width and angles of ribbons, etc), others were more geometric or combinatorial in nature:

  • Can we predict the geometric pattern we will get?
  • How does the number of ribbons influence the pattern?
  • How do the colors of ribbons influence the pattern?
  • Can I change the dance to get any pattern I want?

  • This particular mathematical explorations class was run as a learning community partnered with an English composition class (see also our blog about other aspects of this learning communities ). As one of the writing projects, students were asked to choose a topic connected to mathematics and use it to convince their (chosen) audience that mathematics was cool/beautiful/interesting/worthwhile. One of the students, Sarah Dunn, chose to write for this blog. You can find her work here. She beautifully connects the process of mathematics to the process of running and used our maypole dance activity as evidence in her argument (click on blog below).

    Students dancing around a maypole in their mathematics class.

    Sarah Dunn, student in the Honors Learning Community for "Mathematical Explorations" and "English Composition," reflects on connections between the challenges of running and grappling with the mathematics of maypole dancing. She sees connections in the role played by community support, the thrill of venturing into the unknown, and the passion in pursuing a personal challenge.

    During our class, the students discovered several ways to predict if two choices of ribbons will lead to the "same" geometric pattern or not. Our goal was to predict how many different geometric patterns one can get when 6 people are dancing using different ribbon color combinations. While our conjectures helped reduce the number of different geometric patterns we were not able to completely answer the question yet.

    To get a sense of the complexity of the mathematical arguments, I invite you to look at some student work: an introduction to maypole dancing and a proof of some interesting conjectures we found.

    STEAM exhibit

    In Spring 2017, Westfield State University will host a STEAM exhibit on campus. The students of our learning community prepared an interactive exhibit piece in which the visitors can dance the maypole dance and are invited to think about the mathematics. The students also interviewed themselves to show the visitors what it was like to do mathematics in our class: