A “Paperclip” Approach to Curvature, Torsion, and the Frénet-Serret Formulas

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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

DOI: http://dx.doi.org/10.4169/193113409X469550

Publication date: March 1, 2009

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