Balloon net discovering improved solutions in one of unsolved problems in geometry: A problem of spreading points in a unit square

Kimiya Fujisawa, Yoshiyasu Takefuji

Research output: Contribution to conferencePaper

1 Citation (Scopus)

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 languageEnglish
Pages2208-2210
Number of pages3
Publication statusPublished - 1995 Dec 1
EventProceedings of the 1995 IEEE International Conference on Neural Networks. Part 1 (of 6) - Perth, Aust
Duration: 1995 Nov 271995 Dec 1

Other

OtherProceedings of the 1995 IEEE International Conference on Neural Networks. Part 1 (of 6)
CityPerth, Aust
Period95/11/2795/12/1

ASJC Scopus subject areas

  • Software

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    Fujisawa, K., & Takefuji, Y. (1995). 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, .