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Counting the number of bounded domains separated by hyperplanes
https://hiroshima.repo.nii.ac.jp/records/2006976
https://hiroshima.repo.nii.ac.jp/records/2006976ce013c8c-522c-497f-b759-6a6bb911c50c
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
HiroshimaJMathEduc_7_55.pdf (441.5 KB)
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| Item type | デフォルトアイテムタイプ_（フル）(1) | |||||||
|---|---|---|---|---|---|---|---|---|
| 公開日 | 2023-03-18 | |||||||
| タイトル | ||||||||
| タイトル | Counting the number of bounded domains separated by hyperplanes | |||||||
| 言語 | en | |||||||
| 作成者 |
Imaoka, Mitsunori
× Imaoka, Mitsunori
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| アクセス権 | ||||||||
| アクセス権 | open access | |||||||
| アクセス権URI | http://purl.org/coar/access_right/c_abf2 | |||||||
| 主題 | ||||||||
| 主題Scheme | NDC | |||||||
| 主題 | 370 | |||||||
| 内容記述 | ||||||||
| 内容記述 | 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. | |||||||
| 言語 | en | |||||||
| 出版者 | ||||||||
| 出版者 | Department of Mathematics Education, Faculty of Education, Hiroshima University | |||||||
| 言語 | ||||||||
| 言語 | eng | |||||||
| 資源タイプ | ||||||||
| 資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||||
| 資源タイプ | departmental bulletin paper | |||||||
| 出版タイプ | ||||||||
| 出版タイプ | VoR | |||||||
| 出版タイプResource | http://purl.org/coar/version/c_970fb48d4fbd8a85 | |||||||
| 収録物識別子 | ||||||||
| 収録物識別子タイプ | ISSN | |||||||
| 収録物識別子 | 0919-1720 | |||||||
| 収録物識別子 | ||||||||
| 収録物識別子タイプ | NCID | |||||||
| 収録物識別子 | AN10444573 | |||||||
| 開始ページ | ||||||||
| 開始ページ | 55 | |||||||
| 書誌情報 |
Hiroshima journal of mathematics education Hiroshima journal of mathematics education 巻 7, p. 55-62, 発行日 1999-03 |
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| 旧ID | 29289 | |||||||
