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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/10171
Title: | 三腳架構形之研究與探討 Tripod Configurations |
Authors: | Yu-Ling Wang 王育齡 |
Advisor: | 王藹農(Ai-Nung Wang) |
Keyword: | 三腳架構形, Tripod Configurations, |
Publication Year : | 2011 |
Degree: | 碩士 |
Abstract: | 這篇論文在探討三腳架構形,根據Serge Tabachnikov在附錄[1]的第二個定理:給定一個平滑凸閉平面曲線,至少存在兩個三角架構形。我們在這篇論文中想用跟Serge Tabachnikov不太相同的方法去建構三腳架構形,使用另一種比較直覺的幾何去建構出來。我們採取的方法是minimax method,建造一些變形使Y形的距離和漸漸縮短,但不是所有的Y形均會退化,而會收斂到一個沒有退化的臨界點,再說明臨界點即為我們要的三腳架構形。 In this paper, we research the tripod configurations. By Serge Tabachnikov, see Theorem 2 of Appendix [1] says that for any smooth convex closed curve, there exist at least two tripod configurations. In this paper we want to use another way to construct tripod configurations. Use a intuitive way by a geometrical approach to construct it. We use minimax method, and do some deformation such that the distance of the Y-shaped will decrease, but not all of the Y-shaped will degenerate, it will converge to a critical point which will not degenerate, and we explain that this critical point is our tripod configuration. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/10171 |
Fulltext Rights: | 同意授權(全球公開) |
Appears in Collections: | 數學系 |
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ntu-100-1.pdf | 420.87 kB | Adobe PDF | View/Open |
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