- 學位論文
平面與橢球交集的面積
The area of the intersection of a plane with an ellipsoid
摘要
本論文主旨在推廣橢圓弦長公式，以及平面與橢求交集之橢圓面積公式至高維度的情形。 我們使用一實矩陣計算實對稱矩陣的對角化理論，以及多變數函數的積分變數變換。 其中Gamma函數與Beta函數也被用到作為求出高維度空間中的球體體積的工具。
關鍵字
橢球並列摘要
The purpose of this thesis is to generalize the formula of the length of an chord of an ellipse and the formula of the area of the ellipse which is the intersection of a plane with an ellipsoid. We slove this problems by using some true computation. The theory of diagonalization of real symmetric matrics, and change variable method in integration of functions of several variables. The Gamma and Beta functions are also discussed and used to compute the volume of balls in higher dimensional spaces.
並列關鍵字
ellipsoid參考文獻
1.R.A. Beauregard and J.B. Fraleigh.A first course in linear algebra, Houghton Mifflin, Boston, 1973.
2.S.N. Lee and M.S.Shin, A volume problem for an n-dimensional ellipsoid intersecting with a hyper plane, Linear algebra and its applications 132, 93-102, 1990.
3.Robb J. Muirhead, Aspects of multivariate statistical theory, John wily and sons.
延伸閱讀
- 鄭宜昌（2011）。空間中以直線繪製橢球方法〔碩士論文，國立臺灣大學〕。華藝線上圖書館。https://doi.org/10.6342/NTU.2011.10463
- Lin, H. M. (2010). 在隨機介質中橢圓方程之均質化 [master's thesis, National Chiao Tung University]. Airiti Library. https://doi.org/10.6842/NCTU.2010.00628
- 賴士翔（2001）。凸體與橢球〔碩士論文，中原大學〕。華藝線上圖書館。https://doi.org/10.6840/cycu200100038
- Su, B. Y. (2010). 橢圓曲線上有理點的質階數 [master's thesis, National Taiwan University]. Airiti Library. https://doi.org/10.6342/NTU.2010.03195
- Ali, R. M., Jain, N. K., & Ravichandran, V. (2013). On the Largest Disc Mapped by Sum of Convex and Starlike Functions. Abstract and Applied Analysis, 2013(), 826-837-881. https://doi.org/10.1155/2013/682413