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ERIC Number: EJ853594
Record Type: Journal
Publication Date: 2009-Sep
Pages: 8
Abstractor: ERIC
Reference Count: 6
ISSN: ISSN-0025-5769
Listening to Geometry
Cooper, Brett D.; Barger, Rita
Mathematics Teacher, v103 n2 p108-115 Sep 2009
The many connections between music and mathematics are well known. The length of a plucked string determines its tone, the time signature of a piece of music is a ratio, and note durations are measured in fractions. One connection commonly overlooked is that between music and geometry--specifically, geometric transformations, including translations, rotations, reflections, and dilations. Composers have been using these transformations for centuries. J. S. Bach used translations to structure his fugues, Johann Pachelbel included reflections in his "Canon in D Major," Igor Stravinsky incorporated rotations in "Epitaphium," and the contemporary composer Charles Wuorinen has used dilations. The music connection holds great potential for the high school geometry classroom. High school students' passion for music can be a great motivational tool: The music connection can easily be personalized to individual student tastes, and it provides an application to life as well as a link to another discipline. Studying geometric transformations in music--a real-world application of mathematics--deepens students' understanding of the underlying principles. This article shows how composers use geometric transformations in their music and provides some activities that teachers can use in their classroom. (Contains 10 figures.)
National Council of Teachers of Mathematics. 1906 Association Drive, Reston, VA 20191-1502. Tel: 800-235-7566; Tel: 703-620-3702; Fax: 703-476-2970; e-mail:; Web site:
Publication Type: Journal Articles; Reports - Descriptive
Education Level: High Schools
Audience: Teachers
Language: English
Sponsor: N/A
Authoring Institution: N/A