An Easier Derivation of the Curvature Formula from First Principles

Autor/in	Ferguson, Robert
Titel	An Easier Derivation of the Curvature Formula from First Principles
Quelle	In: Australian Senior Mathematics Journal, 32 (2018) 2, S.16-22 (7 Seiten) PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0819-4564
Schlagwörter	Mathematics Education; Algebra; Geometry; Mathematical Logic; Mathematical Formulas; Problem Solving; Mathematics Instruction; Teaching Methods; Secondary School Mathematics; College Mathematics + Suchen Sie Ihr Suchwort? Mathematische Bildung; Geometrie; Mathematical logics; Mathematische Logik; Mathematische Formel; Problemlösen; Mathematics lessons; Mathematikunterricht; Teaching method; Lehrmethode; Unterrichtsmethode
Abstract	The radius of curvature formula is usually introduced in a university calculus course. Its proof is not included in most high school calculus courses and even some first-year university calculus courses because many students find the calculus used difficult (see Larson, Hostetler and Edwards, 2007, pp. 870- 872). Fortunately, there is an easier way to motivate and prove the radius of curvature formula without using formal calculus. An additional benefit is that the proof provides the coordinates of the centre of the corresponding circle of curvature. Understanding the proof requires only what advanced high school students already know: e.g., algebra, a little geometry about circles, and the intuition that both a circle and a curve have a slope and curvature. The proof is suitable for first-year university and advanced high school students. (As Provided).
Anmerkungen	Australian Association of Mathematics Teachers (AAMT). GPO Box 1729, Adelaide 5001, South Australia. Tel: +61-8-8363-0288; Fax: +61-8-8362-9288; e-mail: office@aamt.edu.au; Web site: http://www.aamt.edu.au
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2021/2/06