Counting the number of bounded domains separated by hyperplanes
Hiroshima journal of mathematics education 7 巻
55-62 頁
1999-03 発行
アクセス数 : 861 件
ダウンロード数 : 93 件
今月のアクセス数 : 5 件
今月のダウンロード数 : 2 件
この文献の参照には次のURLをご利用ください : https://ir.lib.hiroshima-u.ac.jp/00029289
| ファイル情報(添付) | |
| タイトル ( eng ) |
Counting the number of bounded domains separated by hyperplanes
|
| 作成者 | |
| 収録物名 |
Hiroshima journal of mathematics education
|
| 巻 | 7 |
| 開始ページ | 55 |
| 終了ページ | 62 |
| 抄録 |
When some hyperplanes H_1, ..., H_m of the n-dimensional Euclidean space R^n are given in general position, Schläfli has determined the number of the bounded connected components in R^n - ∪^m_i = _1H_i, the complementary set of the union of the hyperplanes. It is equal to the binomial coefficient ((m-1)/n), which is also equal to the number of vertices which are the intersections of n hyperplanes in H_1, ..., H_<m-1>. Although Schläfli's proof is implicit and intuitive, the fact reflects an interesting aspect concerning configurations of hyperplanes. We clarify how the condition of general position works, and re-prove the fact in all of its details.
|
| NDC分類 |
教育 [ 370 ]
|
| 言語 |
英語
|
| 資源タイプ | 紀要論文 |
| 出版者 |
Department of Mathematics Education, Faculty of Education, Hiroshima University
|
| 発行日 | 1999-03 |
| 出版タイプ | Version of Record（出版社版。早期公開を含む） |
| アクセス権 | オープンアクセス |
| 収録物識別子 |
[ISSN] 0919-1720
[NCID] AN10444573
|
