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A Diophantine Equation from Calculus

by George P. Graham (Indiana State University) and Charles E. Roberts (Indiana State University)

This article originally appeared in:
Mathematics Magazine
April, 1989

Subject classification(s): Single Variable Calculus | Calculus | Diophantine Equations | Number Theory | Algebra | Algebra and Number Theory
Applicable Course(s): 4.3 Number Theory | 3.4 Non-mainstream Calc I | 3.1 Mainstream Calculus I | 3.0 Calculus

This article revisits the famous calculus optimization problem of removing four corner squares from a sheet and folding up the edges to form a box of maximal volume. The authors analyze the possible choice of positive integer dimensions of the sheet that result in a maximal box with rational volume.

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Capsule Course Topic(s):
One-Variable Calculus | Differentiation: General Applications
Number Theory | Diophantine Problems
Number Theory | Divisibility
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