Mathematics and the Ballet Barre

Karl Schaffer
Proceedings of Bridges 2012: Mathematics, Music, Art, Architecture, Culture (2012)
Pages 529–532


The ballet barre is a standard set of exercises at the beginning of the traditional ballet class, and is usually composed of a small number of movements and positions arranged according to established constraints and format. In this paper we simplify and examine some mathematical properties of these exercises, focusing on the movement known as tendu, examine some connections to the Fibonacci numbers, and set up a finite-state automaton as a means of visualizing the exercises.