两个单形混合顶点角的广义正弦定理及应用

doi:10.13371/j.cnki.chin.q.j.m.2015.02.005

数学季刊 ›› 2015, Vol. 30 ›› Issue (2): 190-198.doi: 10.13371/j.cnki.chin.q.j.m.2015.02.005

两个单形混合顶点角的广义正弦定理及应用

School of Mathematics and Statistics, Hefei Normal University

收稿日期:2013-05-07 出版日期:2015-06-30 发布日期:2020-11-23
作者简介:WANG Wen(1985-), male, native of Zongyang, Anhui, an assistant of Hefei Normal University, M.S.D., engages in convex and distance geometry; YANG Shi-guo(1952-), male, native of Mingguang, Anhui, a professor of Hefei Normal University, engages in convex and distance geometry.
基金资助:
Supported by the Doctoral Programs Foundation of Education Ministry of China(20113401110009)； Supported by the Universities Natural Science Foundation of Anhui Province(KJ2013A220)； Supported by the Natural Science Research Project of Hefei Normal University(2012kj11)；

The Generalized Sine Theorem for Mixed Vertex Angle of Two Simplices and Applications

School of Mathematics and Statistics, Hefei Normal University

Received:2013-05-07 Online:2015-06-30 Published:2020-11-23
About author:WANG Wen(1985-), male, native of Zongyang, Anhui, an assistant of Hefei Normal University, M.S.D., engages in convex and distance geometry; YANG Shi-guo(1952-), male, native of Mingguang, Anhui, a professor of Hefei Normal University, engages in convex and distance geometry.
Supported by:
Supported by the Doctoral Programs Foundation of Education Ministry of China(20113401110009)； Supported by the Universities Natural Science Foundation of Anhui Province(KJ2013A220)； Supported by the Natural Science Research Project of Hefei Normal University(2012kj11)；

摘要/Abstract

摘要： Some related problems of two n-dimensional simplices which are on an（n- 1）-dimensional hypersphere are investigated and a sine theorem of the k-dimensional mixed vertex angles which are defined in this paper is given. This result is a generalization of the sine theorem established. By using the generalized sine theorem, we present some new interesting geometric inequalities involving the k-dimensional vertex angles of each n-simplex and the k-dimensional mixed vertex angle of two n-simplices. These results can improve some recent results.

关键词: simplex, k-dimensional vertex angle, k-dimensional mixed vertex angle, the sine theorem, geometric inequalities

Abstract: Some related problems of two n-dimensional simplices which are on an（n- 1）-dimensional hypersphere are investigated and a sine theorem of the k-dimensional mixed vertex angles which are defined in this paper is given. This result is a generalization of the sine theorem established. By using the generalized sine theorem, we present some new interesting geometric inequalities involving the k-dimensional vertex angles of each n-simplex and the k-dimensional mixed vertex angle of two n-simplices. These results can improve some recent results.

Key words: simplex, k-dimensional vertex angle, k-dimensional mixed vertex angle, the sine theorem, geometric inequalities

中图分类号:

O182

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.

WANG Wen, YANG Shi-guo, QI Ji-bing. The Generalized Sine Theorem for Mixed Vertex Angle of Two Simplices and Applications[J]. Chinese Quarterly Journal of Mathematics, 2015, 30(2): 190-198.

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两个单形混合顶点角的广义正弦定理及应用

The Generalized Sine Theorem for Mixed Vertex Angle of Two Simplices and Applications

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