ERIC Number: EJ862220
Record Type: Journal
Publication Date: 2009-Mar
Abstractor: As Provided
Reference Count: 0
A "Paperclip" Approach to Curvature, Torsion, and the Frenet-Serret Formulas
Hoensch, Ulrich A.
College Mathematics Journal, v40 n2 p113-118 Mar 2009
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.
Descriptors: Equations (Mathematics), Calculus, Geometric Concepts, Mathematics Instruction, College Mathematics, Mathematical Concepts, Mathematical Formulas, Graphs, Problem Solving, Computer Uses in Education, Topology, Teaching Methods
Mathematical Association of America. 1529 Eighteenth Street NW, Washington, DC 20036. Tel: 800-741-9415; Tel: 202-387-5200; Fax: 202-387-1208; e-mail: firstname.lastname@example.org; Web site: http://www.maa.org/pubs/cmj.html
Publication Type: Journal Articles; Reports - Evaluative
Education Level: Higher Education
Authoring Institution: N/A