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

研究成果: Paper査読

1 被引用数 (Scopus)

抄録

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.

本文言語English
ページ2208-2210
ページ数3
出版ステータスPublished - 1995 12月 1
イベントProceedings of the 1995 IEEE International Conference on Neural Networks. Part 1 (of 6) - Perth, Aust
継続期間: 1995 11月 271995 12月 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

  • ソフトウェア

フィンガープリント

「Balloon net discovering improved solutions in one of unsolved problems in geometry: A problem of spreading points in a unit square」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル