Representing Geometric Constructions As Programs: A Brief Exploration

This column will publish short (ranging from just a few paragraphs to ten or so pages), lively and intriguing computer-related mathematics vignettes. These vignettes or snapshots should illustrate ways in which computer environments have transformed the practice of mathematics or mathematics pedagogy. They could also include puzzles or brain teasers involving the use of computers or computational theory. Snapshots are subject to peer review. In this issue’s snapshot, Bruce Sherin presents a series of geometric constructions made in a Boxer programming environment enriched with a modest set of primitives. In reflecting on the resultant blended turtle geometric and dynamic geometry environment, he discusses the role and potential of programmable applications and the affordances of a programming representation of geometric concepts and other sub-domains of mathematics.