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

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 project is funded by the National Science Foundation's (NSF's) Advancing Informal STEM Learning (AISL) program, which supports innovative research, approaches, and resources for use in a variety of learning settings.

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