A “Paperclip” Approach to Curvature, Torsion, and the Frénet-Serret Formulas
Author: Hoensch, Ulrich A.
Source: The College Mathematics Journal, Volume 40, Number 2, March 2009 , pp. 113-118(6)
Publisher: Mathematical Association of America
Abstract:We explore how curvature and torsion determine the shape of a curve via the Frenet-Serret formulas. The connection is made explicit using the existence of solutions to ordinary differential equations. We use a paperclip as a concrete, visual example and generate its graph in 3-space using a CAS. We also show how certain physical deformations to the paperclip (e.g. bending) can easily be incorporated in the differential equations.
Document Type: Research Article
Publication date: March 1, 2009
- 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.
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