### Abstract

This note shows that in terms of known proofs of the Besicovitch Covering Theorem, the best constant for that theorem is the maximum number of points that can be packed into a closed ball of radius 2 when the distance between pairs of points is at least 1 and one of the points is at the center of the ball. Exponential upper and lower bounds are also established.

Original language | English |
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Pages (from-to) | 1063-1073 |

Number of pages | 11 |

Journal | Proceedings of the American Mathematical Society |

Volume | 121 |

Issue number | 4 |

DOIs | |

Publication status | Published - 1994 |

### Fingerprint

### Keywords

- Besicovitch Covering Theorem
- Proximity graphs
- Sphere packings

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Proceedings of the American Mathematical Society*,

*121*(4), 1063-1073. https://doi.org/10.1090/S0002-9939-1994-1249875-4

**On the best constant for the besicovitch covering theorem.** / Füredi, Z.; Loeb, Peter A.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 121, no. 4, pp. 1063-1073. https://doi.org/10.1090/S0002-9939-1994-1249875-4

}

TY - JOUR

T1 - On the best constant for the besicovitch covering theorem

AU - Füredi, Z.

AU - Loeb, Peter A.

PY - 1994

Y1 - 1994

N2 - This note shows that in terms of known proofs of the Besicovitch Covering Theorem, the best constant for that theorem is the maximum number of points that can be packed into a closed ball of radius 2 when the distance between pairs of points is at least 1 and one of the points is at the center of the ball. Exponential upper and lower bounds are also established.

AB - This note shows that in terms of known proofs of the Besicovitch Covering Theorem, the best constant for that theorem is the maximum number of points that can be packed into a closed ball of radius 2 when the distance between pairs of points is at least 1 and one of the points is at the center of the ball. Exponential upper and lower bounds are also established.

KW - Besicovitch Covering Theorem

KW - Proximity graphs

KW - Sphere packings

UR - http://www.scopus.com/inward/record.url?scp=0042306345&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0042306345&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-1994-1249875-4

DO - 10.1090/S0002-9939-1994-1249875-4

M3 - Article

AN - SCOPUS:0042306345

VL - 121

SP - 1063

EP - 1073

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 4

ER -