Using Star Polygons to Understand Cyclic Group Structure

Sandy Spitzer
Proceedings of Bridges 2012: Mathematics, Music, Art, Architecture, Culture (2012)
Pages 479–480 Short Papers


The study of abstract groups is a challenging one for many undergraduate students. In this paper, we present an overview of a geometric context which can help students interpret and understand the structure of cyclic groups, as well as gain a broader conceptual understanding of such central ideas as subgroups and cosets. The authentic artistic context of star polygons can both motivate students to persist in a search for patterns and provide a concrete referent from which students can generalize algebraic ideas.