Mathematics in Visual Art and Ballet

honors thesisCollege of ScienceMathematicsMaggie CummingsCultures all over the globe utilize both mathematics and ballet to understand the world and to express their distinct realities. In this way, mathematics and art interact, both with math creating new visual art fields, like fractal artworks, and with art influencing mathematics, as with Renaissance painters' use of perspective resulting in the invention of projective geometry. Mathematicians also link math and music, through scale proportions and equations describing harmony. Existing analysis of classical ballet through a mathematical lens, however, is lacking. Current journal articles acknowledge the geometric aesthetic that ballet utilizes and consider how ballet barre combinations can be analyzed as sequences, creating unique patterns through rhythm, direction, and repetition. No apparent literature exists examining the great classical ballet choreographies, particularly considering the large formations created by the corps de ballet. Over my years as a ballet performer and admirer and through my studies of mathematics, I naturally saw these large formations as dynamic differential equations, particularly in Swan Lake's corps de ballet. Through my study of differential equations and dynamical systems, I believe that some of these equations can be classified as useful in dance choreographies, and these equations likely have some identifiable mathematical similarity. I believe this is an area for possible future research that could result in the future creation of choreography based in mathematical concepts