| 关于内接单形的不等式及其应用 |
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| 引用本文： | 潘娟娟,杨世国. 关于内接单形的不等式及其应用[J]. 数学的实践与认识, 2011, 41(15) |
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| 作者姓名： | 潘娟娟 杨世国 |
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| 作者单位： | 1. 安徽大学数学科学学院,安徽合肥230039;安徽新华学院公共课教学部,安徽合肥230088
2. 合肥师范学院数学系,安徽合肥,230061 |
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| 基金项目： | 国家自然基金项目(60671051); 安徽省高校省级重点项目(KJ52009A45) |
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| 摘 要： | 应用解析方法和几何不等式理论研究了n维欧氏空间E~n中涉及n维单形Ω_n与其内接单形Ω′_n的几何不等式的问题,建立了涉及单形Ω_n及其内接单形Ω′_n的外接球半径与高线的一类几何不等式,作为其特例得到了著名的n维Euler不等式的一些推广.
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| 关 键 词： | 单形 外接球半径 高线 内点 不等式 |
Geometric Inequalities And Their Applications For Inscribed Simplex |
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| PAN Juan-juan,YANG Shi-guo. Geometric Inequalities And Their Applications For Inscribed Simplex[J]. Mathematics in Practice and Theory, 2011, 41(15) |
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| Authors: | PAN Juan-juan YANG Shi-guo |
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| Affiliation: | PAN Juan-juan~(1,2),YANG Shi-guo~3 (1.School of Mathematical Sciences,Anhui University,Hefei 230039,China) (2.Department of Basic Courses,Xinhua College,Hefei 230088,China) (3.Department of Mathematical,Hefei Teachers College,Hefei 230061,China) |
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| Abstract: | Using analytic method and theory of geometric inequality,we study the problem of geometric inequalities concerning n-dimensional simplexΩ_n and its inscribed simplexΩ'_n in E~n.Some geometric inequalities for the circumradius ofΩ_n andΩ'_n and altitude are established.As the special case,some generalizations of the famous n-dimensional Euler inequality were obtained. |
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| Keywords: | simplex circumradius altitude interior point inequality |
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