## Functional Geometry and the Traite Ì de Lutherie

Functional Geometry and the Traite Ì de Lutherie by Harry Mairson, Brandeis University.

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 Francois Denisâ€™s book, Traite Ì de lutherie. The programming vernacular for Denisâ€™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.

## Comment viewing options

The tradition from which such cool stuff comes from is not hard to guess. As I expected the code is in Scheme.

### The Galison paper in fn. 8

The Galison paper in fn. 8 is a very nice piece on intellectual history, if that's your kind of thing.

### It's a great topic

I haven't read the book, but it's a great topic, given the stereotype that the Logical Positivists only cared about science.

### It's an article, not a book,

It's an article, not a book, so much less intimidating.

Thanks!

### UTF-8

Do you know that people have fought and died for UTF-8? This is 2014, and the french word in the title is spelled â€œTraitÃ©â€.

### I believe we signed a treaty

I believe we signed a treaty (or is that traitÃ©?) with the French after we fought last, absolving us of not using accents whenever we can't figure out how to type them.