Functional geometry and the Traité de Lutherie: functional pearl

Abstract

We describe a functional programming approach to the design of outlines of eighteenth-century string instruments. The approach is based on the research described in François Denis's book, Traité de lutherie. The programming vernacular for Denis's instructions, which we call functional geometry, is meant to reiterate the historically justified language and techniques of this musical instrument design. The programming metaphor is entirely Euclidean, involving straightedge and compass constructions, with few (if any) numbers, and no Cartesian equations or grid. As such, it is also an interesting approach to teaching programming and mathematics without numerical calculation or equational reasoning.