**ERIC Number:**EJ875471

**Record Type:**Journal

**Publication Date:**2004

**Pages:**2

**Abstractor:**As Provided

**Reference Count:**0

**ISBN:**N/A

**ISSN:**ISSN-0740-8404

The Open Box Problem

Gearhart, William B.; Shultz, Harris S.

AMATYC Review, v25 n2 p72-73 Spr 2004

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.

Descriptors: Geometric Concepts, Calculus, Mathematics Instruction, College Mathematics, Community Colleges, Mathematical Concepts, Problem Solving

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

**Publication Type:**Journal Articles; Reports - Descriptive

**Education Level:**Two Year Colleges

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A