欧氏空间En中Euler不等式的加强推广

数学季刊 ›› 2012, Vol. 27 ›› Issue (2): 218-223.

欧氏空间En中Euler不等式的加强推广

1. Department of Mathematics, Hefei Normal University 2. School of Mathematical Sciences, Anhui University

收稿日期:2010-07-02 出版日期:2012-06-30 发布日期:2023-03-29
作者简介:WANG Wen(1985-), mail, native of Zongyang, Anhui, engages in convex geometry and distance geometry.
基金资助:
Supported by the National Science Foundation of China(60671051)； Supported by the Foundation of Anhui Higher School(KJ2009A45)

Generalizations of Euler Inequality in the n-dimensional Euclidean Space

1. Department of Mathematics, Hefei Normal University 2. School of Mathematical Sciences, Anhui University

Received:2010-07-02 Online:2012-06-30 Published:2023-03-29
About author:WANG Wen(1985-), mail, native of Zongyang, Anhui, engages in convex geometry and distance geometry.
Supported by:
Supported by the National Science Foundation of China(60671051)； Supported by the Foundation of Anhui Higher School(KJ2009A45)

摘要/Abstract

摘要： The relation between the circum-radius and the in-radius of an n-dimensional simplex in En is studied. Two new generalizations of Euler inequality for the n-dimensional simplex are established. Besides, we obtain some stronger generalizations of Euler inequality for the n-dimensional simplex than previously known results.

关键词: Euclidean space, simplex, circum-radius, in-radius, altitude, Euler inequality

Abstract: The relation between the circum-radius and the in-radius of an n-dimensional simplex in En is studied. Two new generalizations of Euler inequality for the n-dimensional simplex are established. Besides, we obtain some stronger generalizations of Euler inequality for the n-dimensional simplex than previously known results.

Key words: Euclidean space, simplex, circum-radius, in-radius, altitude, Euler inequality

中图分类号:

O184

王文, 杨世国. 欧氏空间En中Euler不等式的加强推广[J]. 数学季刊, 2012, 27(2): 218-223.

WANG Wen, YANG Shi-guo. Generalizations of Euler Inequality in the n-dimensional Euclidean Space[J]. Chinese Quarterly Journal of Mathematics, 2012, 27(2): 218-223.

[1]	周永国. 球面空间单形的两个几何不等式[J]. 数学季刊, 2019, 34(2): 204-208.
[2]	王文, 杨世国, 齐继兵. 两个单形混合顶点角的广义正弦定理及应用[J]. 数学季刊, 2015, 30(2): 190-198.
[3]	杨世国, 王文. 有关单形旁切球半径的几何不等式[J]. 数学季刊, 2015, 30(1): 137-143.
[4]	张晗方. 关于一个单形及其子单形的内切球半径的一些几何不等式[J]. 数学季刊, 2014, 29(2): 215-220.
[5]	周永国. 有限点集的m级连心线及其性质[J]. 数学季刊, 2014, 29(2): 247-252.
[6]	曾建国. 高维单形的等距共轭点性质初探[J]. 数学季刊, 2013, 28(1): 77-81.
[7]	国起. 一般凸体与单形间Banach-Mazur距离估计的一种简单方法[J]. 数学季刊, 2012, 27(4): 504-508.
[8]	周永国. 涉及两个单形及其内点的几个不等式[J]. 数学季刊, 2011, 26(4): 628-632.
[9]	张春苟. 单纯形上积分型Stancu算子在L_p中的逼近逆定理[J]. 数学季刊, 2006, 21(1): 4-9.
[10]	石焕南, 李大矛. Adamovic's不等式的推广与加细[J]. 数学季刊, 2004, 19(1): 35-40.