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| 关于单形及内接单形的几何不等式及应用 | |
| 引用本文： | 孙玉婷,齐继兵,杨世国. 关于单形及内接单形的几何不等式及应用[J]. 合肥学院学报(自然科学版), 2012, 22(3): 17-20 |
| 作者姓名： | 孙玉婷 齐继兵 杨世国 |
| 作者单位： | 1. 安徽大学数学科学学院,合肥,230601 2. 合肥师范学院数学系,合肥,230601 3. 合肥师范学院数学系,合肥230601 安徽新华学院,合肥230088 |
| 基金项目： | 高校博导基金项目，安徽省高等院校省级自然科学研究项目 |
| 摘 要： | 运用代数方法和几何不等式理论,研究了有关单形内点及其内接单形的极值问题,建立了涉及单形及其内接单形的外接球半径以及内点到侧面距离之间的几何不等式.作为特例,对著名的n维Euler不等式作了新的推广和改进. |
| 关 键 词： | 单形 几何不等式 内接单形 Euler不等式 外接球半径 |
Geometric Inequality and Applications for Simplex and Its Inscribed Simplex |
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| SUN Yu-ting,QI Ji-bing,YANG Shi-guo. Geometric Inequality and Applications for Simplex and Its Inscribed Simplex[J]. Journal of Hefei University(Natural Sciences Edition), 2012, 22(3): 17-20 | |
| Authors: | SUN Yu-ting QI Ji-bing YANG Shi-guo |
| Affiliation: | 1. School of Mathematical Sciences,Anhui University, Hefei 230601 ; 2. Department of Mathematics, Hefei Normal University, Hefei 230601;3. Anhui Xinhua University, Hefei 230088, China) |
| Abstract: | The extremum problem of simplex interior point and inscribed simplex is researched, by using analytic method and theory of geometric inequality. A geometric inequality for distance of interior point to side faces of simplex and for the circumradius of simplex and its inscribed simplex is established, which is new improvement of Euler inequality as application. |
| Keywords: | simplex geometric inequality inscribed simplex Euler inequality circumradius. |
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