Dancing Deformations

Karl Schaffer
Proceedings of Bridges 2014: Mathematics, Music, Art, Architecture, Culture (2014)
Pages 253–260


The performing art of dance employs symmetry in a variety of ways. Often choreographers blur the lines between symmetries or seamlessly morph from one symmetry type to another. This may be seen to be similar to parquet deformations, visual images in which one tiling deforms seamlessly into another. In this paper we look at ways linear or frieze symmetries, common in folk dance and other forms, and planar or wallpaper symmetries used in a variety of dance forms may be switched from one to another in time, with particular attention to the Klein four group. The sequences through danced wallpaper symmetries might make for entertaining mathematical flash mob dances.