The Open Box Problem

Autor/inn/en	Gearhart, William B.; Shultz, Harris S.
Titel	The Open Box Problem
Quelle	In: AMATYC Review, 25 (2004) 2, S.72-73 (2 Seiten) PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0740-8404
Schlagwörter	Geometric Concepts; Calculus; Mathematics Instruction; College Mathematics; Community Colleges; Mathematical Concepts; Problem Solving + Suchen Sie Ihr Suchwort? Elementare Geometrie; Analysis; Differenzialrechnung; Infinitesimalrechnung; Integralrechnung; Mathematics lessons; Mathematikunterricht; Community college; Community College; Problemlösen
Abstract	In a well-known calculus problem, an open top box is to be made from a rectangular piece of material by cutting equal squares from each corner and turning up the sides. The task is to find the dimensions of the box of maximum volume. Typically, the length of the sides of the corners that produces the largest volume turns out to be an irrational number. However, there are examples of non-square rectangles for which this length is a rational number. In this article we show how to generate all cases in which integer values for the dimensions of the rectangle produce rational answers. This provides calculus instructors with several rectangles for which the optimal box has "nice" dimensions. (As Provided).
Anmerkungen	American Mathematical Association of Two-Year Colleges. 5983 Macon Cove, Memphis, TN 38134. Tel: 901-333-4643; Fax: 901-333-4651; e-mail: amatyc@amatyc.org; Web site: http://www.amatyc.org
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10