Functional Geometry and the "Traité de Lutherie"
Functional Geometry and the "Traité de Lutherie"
复制标题
泛函几何和“Traité de Lutherie”
DOI：
10.1145/2500365.2500617
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Mairson, Harry
中科院分区：
文献类型：
--
作者：
Mairson, Harry
我们描述了一个功能性的编程方法来设计十八世纪的弦乐器的轮廓。这种方法是基于弗朗索瓦·丹尼斯的著作《路德的信仰》中所描述的研究。丹尼斯指令的编程语言，我们称之为功能几何，是为了重申这种乐器设计的历史合理的语言和技术。编程隐喻完全是欧几里得的，涉及直尺和罗盘构造，很少（如果有的话）数字，没有笛卡尔方程或网格。因此，它也是一种有趣的方法来教授编程和数学，而无需数值计算或方程式推理。这种基于语言的功能方法的优势在于对仪器设计中常见模式的抽象表征。这些模式不仅包括常见直尺和指南针构造的抽象，还包括仪器设计过程的高阶概念化。我们还讨论了算术，几何，谐波和次谐波比例的作用，以及使用他们的合理逼近。
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 callfunctional 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 tolutherieis 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.