空间三角形外心的判定条件和计算  

Judging Conditions and Computation of Circumcenter of Space Triangle

作　　者：张辉 方晓峰 王静 ZHANG Hui;FANG Xiaofeng;WANG Jing(Department of Basic Courses,Rocket Force University of Engineering,Xi'an 710025,China)

机构地区：[1]火箭军工程大学基础部,陕西西安710025

出　　处：《河南财政金融学院学报（自然科学版）》2024年第3期42-47,共6页Journal of Henan Finance University(Natural Science Edition)

基　　金：陕西省教育厅教育教学改革研究课题一般项目(23BY211)。

摘　　要：研究了空间三角形外心的判定条件和计算问题。首先给出3个关于空间三角形的重要引理,然后利用外心的定义和一个命题,给出了判定外心的6个充分必要条件,最后利用判定条件给出了空间三角形外心坐标的计算公式。旨在让学生更深入地理解和掌握空间三角形外心的判定方法,为空间三角形在工程技术领域中的应用提供技术支撑。The judging conditions and computation of the circumcenter of space triangle are studied.Firstly,three important lemmas about the space triangle are given,then three sufficient and necessary conditions and three necessary conditions for judging the circumcenter are given by using the definition of the circumcenter and one proposition.Finally,the calculation formula of the coordinates of the circumcenter of space triangles is given by using the judging conditions,so that students can have a deeper understanding and mastery of the circumcenter of space triangle,which provides technical support for the application of space triangle in the field of engineering technology.

关 键 词：空间三角形 外心 数量积 向量积 重心 

分 类 号：O182.2[理学—数学]