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Harry Mairson, a computer science professor at Brandeis University, devised a computer lan- guage to draw violins, following the methods of construction used by François Denis in his book “Traité de Lutherie.” In this very engaging talk, Harry presents what he did and the reasoning be- hind it. Interested persons are encouraged to con- tact him, and to get and experiment with his code 

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. The advantage of this language-based, functional approach to lutherie is founded in the abstract characterization of common patterns in instrument design. These patterns include not only the abstraction of common straightedge and compass constructions, but of higher-order conceptualization of the instrument design process. We also discuss the role of arithmetic, geometric, harmonic, and subharmonic proportions, and the use of their rational approximants.