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合同変換による多角形の考察
http://hdl.handle.net/10458/3784
http://hdl.handle.net/10458/37840d139238-c3d7-4d1f-a374-4e8a9e611283
| 名前 / ファイル | ライセンス | アクション |
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1284uda.pdf (2.6 MB)
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| Item type | 学術雑誌論文 / Journal Article(1) | |||||
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| 公開日 | 2012-07-23 | |||||
| タイトル | ||||||
| タイトル | 合同変換による多角形の考察 | |||||
| 言語 | ja | |||||
| タイトル | ||||||
| タイトル | A Study of Polygons by means of Congruent Transformations | |||||
| 言語 | en | |||||
| 言語 | ||||||
| 言語 | jpn | |||||
| 資源タイプ | ||||||
| 資源タイプ | journal article | |||||
| その他（別言語等）のタイトル | ||||||
| その他のタイトル | ゴウドウヘンカン ニヨル タカクケイ ノ コウサツ | |||||
| 言語 | ja-Kana | |||||
| 著者 |
宇田, 廣文
× 宇田, 廣文 |
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| 抄録 | ||||||
| 内容記述タイプ | Abstract | |||||
| 内容記述 | In this paper we study the following i)the structure of polygons by making use of congruent transformations, ii)the concrete constructions of polygons with a given structure of congruent transformations, iii)an investigation of the problem presented by T.W.Shilgalis. Let P be a polygon and G(P) be the set of all congruent transformations of P. Then G(P) is a subgroup of a suitable dihedral group D2 n, where D2n is the dihedral group of a regular polygon of n sides. Therefore, we began with a decision on subgroups of the dihedral group D2n. The outline of conclutions is as follows. (1)We determined the subgroups of the dihedral group D2n and showed the existence of polygons with a given subgroup of the dihedral group D2n as a group of congruent transformations. Moreover, we gave the concrete constructions of polygons with a given group-Structure of congruent transformations. (2)We classified polygons by using groups of congruent transformations and determined the fundamental polygons in a viewpoint of congruent transformations. Moreover, we considered the number of symmetry lines and rotations in polygons, and made these properties clear. (3)T.W.Shilgalis denonted by f(n) the maximum number of symmetry lines in an irregular polygon of n sides and suggested the following: f(n)=the largest divisor of n (except n itself). This fact can be given by considerations in (2). This implies that a concept of groups is useful for investigations of polyogns. (4)Concerning a polygon-in particular a dodecagon-having two given symmetry lines, we examined its properties concretely and determined its group-theoretical structure. |
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| 言語 | en | |||||
| 書誌情報 |
ja : 数学教育学研究紀要 巻 19, p. 177-192, 発行日 1993-03 |
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| 出版者 | ||||||
| 出版者 | 西日本数学教育学会 | |||||
| 言語 | ja | |||||
| 著者版フラグ | ||||||
| 出版タイプ | VoR | |||||
