This paper examines three historical geometric constructions for handcrafting stringed instruments. Using elementary geometry – in particular, triangles – these methods can provide quite good rational approximations to the irrationals that arise from tuning instruments in equal temperament. Interestingly, continued fractions help explain the accuracy of all approximations.
Document Type: Research Article
Publication date: November 1, 2008
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The College Mathematics Journal is designed to enhance classroom learning and stimulate thinking regarding undergraduate mathematics. CMJ publishes articles, short Classroom Capsules, problems, solutions, media reviews and other pieces. All are aimed at the college mathematics curriculum with emphasis on topics taught in the first two years.