|
|||||
|
|
| 常曲率平面上的Crofton公式的一个统一证明 | |
| 引用本文： | 艾万君,曾春那,姜德烁.常曲率平面上的Crofton公式的一个统一证明[J].西南师范大学学报(自然科学版),2012,37(8):37-39. |
| 作者姓名： | 艾万君 曾春那 姜德烁 |
| 作者单位： | 1. 西南大学数学与统计学院,重庆,400715 2. 重庆师范大学数学学院,重庆,400047 3. 商丘师范学院数学与信息科学学院,河南商丘,476000 |
| 摘 要： | 首先将常曲率平面上的正弦定理、第一、第二余弦定理改写为统一的形式,然后通过计算测地线段的测度对常曲率平面上的Crofton公式给出了一个统一的证明. |
| 关 键 词： | Crofton公式 常曲率平面 不变测度 |
A Unified Demonstration of Crofton Formulae on the Plane of Constant Curvature |
|
| AI Wan-jun , ZENG Chun-na , JIANG De-shuo.A Unified Demonstration of Crofton Formulae on the Plane of Constant Curvature[J].Journal of Southwest China Normal University(Natural Science),2012,37(8):37-39. | |
| Authors: | AI Wan-jun ZENG Chun-na JIANG De-shuo |
| Institution: | 1.School of Mathematics and Statistics,Southwest University,Congqing 400715,China;2.College of Mathematics Science,Chongqing Normal University,Congqing 400047,China;3.School of Mathematics and Information Science,Shangqiu Normal University,Shangqiu Henan 476000,Chin |
| Abstract: | In this paper,firstly,we rewrite the law of sine,the first and second law of cosines of a geodesic triangle in the plane of constant curvature as a unified form,then,by computing the measure of the geodesic lines,a unified proof of Crofton formulae in the plane of constant curvature has been derived. |
| Keywords: | Crofton formulae plane of constant curvature invariant measure |
| 本文献已被 CNKI 万方数据 等数据库收录！ | |
| 点击此处可从《西南师范大学学报(自然科学版)》浏览原始摘要信息 | |
| 点击此处可从《西南师范大学学报(自然科学版)》下载免费的PDF全文 | |