Spirograph Patterns and Circular Representations of Rhythm: Exploring Number Theory Concepts Through Visual, Tangible and Audible Representations

Susan Gerofsky, Francisco Gomez, David Rappaport and Godfried Toussaint
Proceedings of Bridges 2009: Mathematics, Music, Art, Architecture, Culture (2009)
Pages 279–286 Regular Papers


This paper offers connections between representations in a number of multisensory modes—visual, tactile and audible/musical—that explore a single underlying conceptual structure of periodicity and factorization. A number line is explored in visual, musical and tactile modes with regard to the relationship between regular periodic rhythms; then spirographic geometric patterns and the visual and musical patterns produced by the use of circular representations of musical rhythms are used to develop initial intuitions and observations. Throughout the process, the concept of conceptually-related multiple (multisensory, multimodal) representations is invoked as a way for mathematics learners to feel, hear and see mathematical concepts in depth.