A "Paperclip" Approach to Curvature, Torsion, and the Frenet-Serret Formulas

Autor/in	Hoensch, Ulrich A.
Titel	A "Paperclip" Approach to Curvature, Torsion, and the Frenet-Serret Formulas
Quelle	In: College Mathematics Journal, 40 (2009) 2, S.113-118 (6 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0746-8342
Schlagwörter	Equations (Mathematics); Calculus; Geometric Concepts; Mathematics Instruction; College Mathematics; Mathematical Concepts; Mathematical Formulas; Graphs; Problem Solving; Computer Uses in Education; Topology; Teaching Methods + Suchen Sie Ihr Suchwort? Equations; Mathematics; Gleichungslehre; Analysis; Differenzialrechnung; Infinitesimalrechnung; Integralrechnung; Elementare Geometrie; Mathematics lessons; Mathematikunterricht; Mathematische Formel; Grafische Darstellung; Problemlösen; Computernutzung; Topologie; Teaching method; Lehrmethode; Unterrichtsmethode
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. (As Provided).
Anmerkungen	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: maahq@maa.org; Web site: http://www.maa.org/pubs/cmj.html
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10