两个单形混合顶点角的广义正弦定理及应用

王文, 杨世国, 齐继兵

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

数学季刊 >

2015 , Vol. 30 >Issue 2: 190 - 198

DOI: https://doi.org/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

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School of Mathematics and Statistics, Hefei Normal University

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.

收稿日期: 2013-05-07

网络出版日期: 2020-11-23

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)；

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

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School of Mathematics and Statistics, Hefei Normal University

Received date: 2013-05-07

Online published: 2020-11-23

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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

本文引用格式

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

Abstract

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

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