### Abstract

Let F be a convex figure with area | F | and let G (n, F) denote the smallest number such that from any n points of F we can get G (n, F) triangles with areas less than or equal to | F | / 4. In this article, to generalize some results of Soifer, we will prove that for any triangle T, G (5, T) = 3; for any parallelogram P, G (5, P) = 2; for any convex figure F, if S (F) = 6, then G (6, F) = 4.

Original language | English (US) |
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Pages (from-to) | 3960-3981 |

Number of pages | 22 |

Journal | Discrete Mathematics |

Volume | 308 |

Issue number | 17 |

DOIs | |

State | Published - Sep 6 2008 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

### Keywords

- Area
- Convex figure
- Heilbronn's problem
- Parallelogram
- Soifer's problem
- Triangle

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## Cite this

Diao, H., Gangsong, L., & Lin, S. (2008). On a Heilbronn-type problem.

*Discrete Mathematics*,*308*(17), 3960-3981. https://doi.org/10.1016/j.disc.2007.07.101