### Abstract

A balloon net model is introduced and demonstrated for discovering improved solutions in one of unsolved problems in geometry which is referred to as a problem of `Spreading points in a square'. How should n points be arranged in a unit square so that the minimum distance between them is the greatest? Note that d(n) is the greatest possible minimum distance between n points in a unit square. Exact results are known for n≤9 and n = 14, 16, 25, and 36. Many investigators including Schaer, Meir, Kirchner, Wengerodt, Goldberg, Schluter, Valette and others have studied this geometrical problem for many years. The best known result is summarized in the book of `Unsolved Problems in Geometry' (H.T. Croft. K.J. Falconer and R.K. Guy/1991). We have found improved solutions for n = 13 and n = 15 by the proposed algorithm.

Original language | English |
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Pages | 2208-2210 |

Number of pages | 3 |

Publication status | Published - 1995 Dec 1 |

Event | Proceedings of the 1995 IEEE International Conference on Neural Networks. Part 1 (of 6) - Perth, Aust Duration: 1995 Nov 27 → 1995 Dec 1 |

### Other

Other | Proceedings of the 1995 IEEE International Conference on Neural Networks. Part 1 (of 6) |
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City | Perth, Aust |

Period | 95/11/27 → 95/12/1 |

### ASJC Scopus subject areas

- Software

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## Cite this

*Balloon net discovering improved solutions in one of unsolved problems in geometry: A problem of spreading points in a unit square*. 2208-2210. Paper presented at Proceedings of the 1995 IEEE International Conference on Neural Networks. Part 1 (of 6), Perth, Aust, .