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

这项跨学科科学与工程推进研究（RAISE）项目得到了教育与人力资源理事会学习研究部和计算机与信息科学与工程理事会计算与通信基础部的支持。这个跨学科项目将文艺复兴时期用于制作古典弦乐器的几何设计原理的历史见解与计算机科学原理的现代见解相结合。本项目以古典弦乐器的制作与设计为例，将抽象的数学概念应用于家具、建筑、绘画和乐器的制作与设计中。这项研究可以帮助乐器制造商使用定制的软件来促进历史设计的比较，这些设计既借鉴了几何证据，也借鉴了艺术史的证据。该项目的影响包括从根本上改变制造商对设计和制作过程的看法，以及计算机科学家如何使用编程语言的基本概念来告知物理对象的表示。此外，本项目还开发了一种替代教学方法，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声学效果等方面为当前的制琴师提供具体指导。该项目开发了一种基于直边和罗盘结构的特定于领域的函数式编程语言，并将其应用于三个互补的方向。第一个方向是开发软件工具（编译器），以文艺复兴时期应用的几何设计原则为基础，为古典弦乐器的构造提供信息。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，并探索了其他制造商领域的扩展。第三个方向是使用特定于领域的语言来设计教育软件工具。该工具使用计算和建设性的方法在大学预科阶段教授欧几里得几何，并补充了传统的代数，基于证明的教学方法。通过高级编程抽象来表示乐器形式也有助于它们的制造，特别是通过使用计算机数控（CNC）方法来关注前后雕刻板的拱形-具有相当大的声学意义。该项目的新颖之处包括领域特定语言本身，这是一种合成几何的可编程形式，很大程度上没有数字；它在当代小提琴制作过程和其他制作领域的应用；它作为计算艺术史的基础，为古典弦乐器设计及其相关物质文化的演变提供了分析性的见解；作为一种建构性的，计算性的几何教学方法。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值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.