### Abstract

We show that if the unit square is covered by n rectangles, then at least one must have perimeter at least 4(2 m+1)/(n+m(m+1)), where m is the largest integer whose square is at most n. This result is exact for n of the form m(m+1) (or m^{2}).

Original language | English (US) |
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Pages (from-to) | 1-7 |

Number of pages | 7 |

Journal | Discrete & Computational Geometry |

Volume | 1 |

Issue number | 1 |

DOIs | |

State | Published - Dec 1 1986 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics

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## Cite this

Alon, N., & Kleitman, D. J. (1986). Covering a square by small perimeter rectangles.

*Discrete & Computational Geometry*,*1*(1), 1-7. https://doi.org/10.1007/BF02187679