RAISE: Software for Making: Programmable Geometry for Mathematics Education, Classical Stringed Instrument Design, and its Material Culture

这项由跨学科科学和工程推动的研究项目由教育和人力资源局的学习研究司和计算机和信息科学与工程局的计算和通信基础司提供支助。这个跨学科的项目将文艺复兴时期用于制作古典弦乐乐器的几何设计原则的历史见解与计算机科学原理的现代见解结合在一起。该项目通过一个具体的例子：古典弦乐器的制造和设计，将抽象的数学概念应用到家具、建筑、绘画和乐器的制造和设计中。这项研究可以帮助仪器制造商使用定制的软件，以便于对历史设计进行比较，这些设计既利用了几何证明，也利用了艺术史上的证据。该项目的影响包括，不仅可能从根本上改变制造者对设计和制造过程的思考方式，而且还可能改变计算机科学家如何使用编程语言中的基本概念来表示物理对象。此外，该项目还开发了一种替代教学方法来帮助学生以创造性的方式理解数学，并在设计弦乐器的物理结构以提高音效等方面为当前的琴师提供具体指导。该项目开发了一种基于直边和指南针结构的特定领域的函数式编程语言，并在三个互补的方向上应用它。第一个方向是开发软件工具(编译器)，以便根据文艺复兴时期应用的几何设计原则建造古典弦乐乐器。第二个方向发展了对这些乐器的艺术史的分析和计算理解，并探索了对其他制造者领域的扩展。第三个方向使用这种特定于领域的语言来设计教育软件工具。该工具使用计算和构造性的方法在大学预科阶段教授欧几里得几何，并补充了传统的基于证明的代数教学方法。通过高级编程抽象来表示乐器形式也方便了它们的制造，特别是通过使用计算机数字控制(CNC)方法，特别关注具有相当大声学意义的前后雕刻板的拱形。该项目的创新之处包括领域特定语言本身，这是一种可编程的合成几何形式，基本上没有数字；它在当代小提琴制造过程和其他制造领域的应用；它作为计算艺术史的基础，提供对古典弦乐设计及其相关材料文化演变的分析见解；以及作为一种构造和计算方法来教授几何。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This Research Advanced by Interdisciplinary Science and Engineering (RAISE) project is supported by the Division of Research on Learning in the Education and Human Resources Directorate and by the Division of Computing and Communication Foundations in the Computer and Information Science and Engineering Directorate. This interdisciplinary project integrates historical insights from geometric design principles used to craft classical stringed instruments during the Renaissance era with modern insights drawn from computer science principles. The project applies abstract mathematical concepts toward the making and designing of furniture, buildings, paintings, and instruments through a specific example: the making and designing of classical stringed instruments. The research can help instrument makers employ customized software to facilitate a comparison of historical designs that draws on both geometrical proofs and evidence from art history. The project's impacts include the potential to shift in fundamental ways not only how makers think about design and the process of making but also how computer scientists use foundational concepts from programming languages to inform the representation of physical objects. Furthermore, this project develops an alternate teaching method to help students understand mathematics in creative ways and offers specific guidance to current luthiers in areas such as designing the physical structure of a stringed instrument to improve acoustical effect.The project develops a domain-specific functional programming language based on straight-edge and compass constructions and applies it in three complementary directions. The first direction develops software tools (compilers) to inform the construction of classical stringed instruments based on geometric design principles applied during the Renaissance era. The second direction develops an analytical and computational understanding of the art history of these instruments and explores extensions to other maker domains. The third direction uses this domain-specific language to design an educational software tool. The tool uses a calculative and constructive method to teach Euclidean geometry at the pre-college level and complements the traditional algebraic, proof-based teaching method. The representation of instrument forms by high-level programming abstractions also facilitates their manufacture, with particular focus on the arching of the front and back carved plates --- of considerable acoustic significance --- through the use of computer numerically controlled (CNC) methods. The project's novelties include the domain-specific language itself, which is a programmable form of synthetic geometry, largely without numbers; its application within the contemporary process of violin making and in other maker domains; its use as a foundation for a computational art history, providing analytical insights into the evolution of classical stringed instrument design and its related material culture; and as a constructional, computational approach to teaching geometry.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.