研究生: |
李函燊 Li, Han-Shen |
---|---|
論文名稱: |
球面上圓的性質 Properties of Circles on Sphere |
指導教授: |
全任重
Chuan, Jen-Chung |
口試委員: |
李華倫
李明恭 |
學位類別: |
碩士 Master |
系所名稱: |
理學院 - 數學系 Department of Mathematics |
論文出版年: | 2012 |
畢業學年度: | 100 |
語文別: | 中文 |
論文頁數: | 25 |
中文關鍵詞: | 球面上的圓 |
相關次數: | 點閱:1 下載:0 |
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My goal is to discover some properties of circles on sphere by inversing some circle theorems on the plane in some sphere, i.e. their stereographic projection respect to some sphere. Since all the graphics lie on the same plane, they will lie on the same ball after inversing to a sphere. And the inversion of a circle is still a circle. Hence, we will obtain some circles on sphere. Then we exam whether it keeps the original properties or generates some new properties. Therefore we will start to construct graphics on the plane first then there should be no difficulties to construct theorems in space. We use Cabri II and Cabri 3D as convenient tools to discover geometric properties. In this article we will discuss about Soddy Circles and Seven Circles Theorem.
[1]Bakel’man, I. IA. (Il’ia Iakovlevich), 1928- . Inversion/ I. Ya. Bakel’man; Translated and adapted from the Russian by Susan Williams and Joan W. Teller, Chicago:University of Chicago Press, 1974
[2] Coxeter, H. S. M. Introduction to Geometry, 2nd Ed. New York: Wiley, 1969
[3] Honsberger, R. "The Symmedian Point." Ch. 7 in Episodes in Nineteenth and Twentieth Century Euclidean Geometry. Washington, DC: Math. Assoc. Amer., pp. 53-77, 1995.
[4] http://mathworld.wolfram.com