Boxes, Pans, and Cans: A Diohpantine Approach to Optimization

Vincent E. Coll; Jeremy Davis; Martin Hall; Colton Magnant; James Stankewicz; Hua Wang

doi:10.4169/college.math.j.45.3.180

Boxes, Pans, and Cans: A Diohpantine Approach to Optimization

Vincent E. Coll, Jeremy Davis, Martin Hall, Colton Magnant, James Stankewicz, Hua Wang

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

Two approaches contribute to the problem of finding integer side-lengths for open rectangular and polygonal boxes that optimize volume. One method adapts Pythagorean triples to an ellipse, while the other is based on counting factorizations.

Original language	American English
Journal	College Mathematics Journal
Volume	45
DOIs	https://doi.org/10.4169/college.math.j.45.3.180
State	Published - Jan 1 2014

Keywords

Ellipse
Factorizations
Integer side-lengths
Pythagorean triples
Volume optimization

DC Disciplines

Education
Mathematics

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https://doi.org/10.4169/college.math.j.45.3.180

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title = "Boxes, Pans, and Cans: A Diohpantine Approach to Optimization",

abstract = " Two approaches contribute to the problem of finding integer side-lengths for open rectangular and polygonal boxes that optimize volume. One method adapts Pythagorean triples to an ellipse, while the other is based on counting factorizations.",

keywords = "Ellipse, Factorizations, Integer side-lengths, Pythagorean triples, Volume optimization",

author = "Coll, {Vincent E.} and Jeremy Davis and Martin Hall and Colton Magnant and James Stankewicz and Hua Wang",

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doi = "10.4169/college.math.j.45.3.180",

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AU - Davis, Jeremy

AU - Hall, Martin

AU - Magnant, Colton

AU - Stankewicz, James

AU - Wang, Hua

PY - 2014/1/1

Y1 - 2014/1/1

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AB - Two approaches contribute to the problem of finding integer side-lengths for open rectangular and polygonal boxes that optimize volume. One method adapts Pythagorean triples to an ellipse, while the other is based on counting factorizations.

KW - Ellipse

KW - Factorizations

KW - Integer side-lengths

KW - Pythagorean triples

KW - Volume optimization

UR - https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/222

UR - https://doi.org/10.4169/college.math.j.45.3.180

U2 - 10.4169/college.math.j.45.3.180

DO - 10.4169/college.math.j.45.3.180

M3 - Article

SN - 0746-8342

VL - 45

JO - College Mathematics Journal

JF - College Mathematics Journal

ER -

Boxes, Pans, and Cans: A Diohpantine Approach to Optimization

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Keywords

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