The decomposition of a square into rectangles of minimal perimeter

T. Y. Kong; David M. Mount; Michael Werman

doi:10.1016/0166-218X(87)90061-8

The decomposition of a square into rectangles of minimal perimeter

T. Y. Kong^*
, David M. Mount
, Michael Werman

^*Corresponding author for this work

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

11 Scopus citations

Abstract

This paper solves the problem of subdividing a unit square into p rectangles of area 1/p in such a way that the maximal perimeter of a rectangle is as small as possible. The correctness of the solution is proved using the well-known theorems of Menger and Dilworth.

Original language	English
Pages (from-to)	239-243
Number of pages	5
Journal	Discrete Applied Mathematics
Volume	16
Issue number	3
DOIs	https://doi.org/10.1016/0166-218X(87)90061-8
State	Published - Mar 1987
Externally published	Yes

Bibliographical note

Funding Information:
* Permanent address: Department of Computer Science, Ohio University, Athens, Ohio 45701. ** The support of the Air Force Office of Scientific Research under Contract F-49620-85-K-0009 is gratefully acknowledged. *** Permanent address: Department of Computer Science, The Hebrew University of Jerusalem, 91904 Jerusalem, Israel.

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10.1016/0166-218X(87)90061-8

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title = "The decomposition of a square into rectangles of minimal perimeter",

abstract = "This paper solves the problem of subdividing a unit square into p rectangles of area 1/p in such a way that the maximal perimeter of a rectangle is as small as possible. The correctness of the solution is proved using the well-known theorems of Menger and Dilworth.",

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note = "Funding Information: * Permanent address: Department of Computer Science, Ohio University, Athens, Ohio 45701. ** The support of the Air Force Office of Scientific Research under Contract F-49620-85-K-0009 is gratefully acknowledged. *** Permanent address: Department of Computer Science, The Hebrew University of Jerusalem, 91904 Jerusalem, Israel.",

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AB - This paper solves the problem of subdividing a unit square into p rectangles of area 1/p in such a way that the maximal perimeter of a rectangle is as small as possible. The correctness of the solution is proved using the well-known theorems of Menger and Dilworth.

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The decomposition of a square into rectangles of minimal perimeter

Abstract

Bibliographical note

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