This project aims to analyze the connections between ballet and mathematics. Specifically, this project focuses on analyzing the three-dimensional surfaces created as a dancer performs ballet choreography. The primary goal is to use a Vicon motion capture system in conjunction with MATLAB to model the three-dimensional lines and surfaces created by a dancer’s legs as she performs specific ballet movements. The movements used for this experiment were a pique turn and a rond de jambe. The data was collected using sensors to create objects in Vicon to record the position of the ankle, knee, and hip of the working leg while the dancer performed specific ballet movements. The position data was first analyzed in Excel, where specific criteria were used to eliminate data points that were incorrect due to errors while recording. Then the position data was exported to MATLAB for analysis. The data points were used to create fitted polynomials through the ankle, knee, and hip. Next, line segments were constructed between the ankle and knee and between the knee and hip. The ultimate goal is to find a closed form equation to mathematically describe the surfaces created by the dancers legs for each move and to find a general model for future experiments.
Gibson, Kendall, "The Mathematical Modeling of Ballet" (2019). Mathematics Senior Capstone Papers. 6.