空间三角形重心的判定条件和算法

Judging Conditions and Computing Method of Gravity Center of Space Triangle

研究了空间三角形重心的判定条件和算法问题。首先给出两个关于空间三角形内点的重要引理,然后利用重心的定义和两个引理,给出了判定重心的3个充分必要条件,最后利用判定条件给出了空间三角形重心坐标的计算公式。旨在让学生对空间三角形的重心有更深入的理解和掌握,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 computing method of the center of gravity of spatial triangle are studied.Firstly,two important lemmas about the interior points of spatial triangles are given,then three sufficient and necessary conditions for judging the center of gravity are given by using the definition of the center of gravity and two lemmas.Finally,the calculation formula of the coordinates of the center of gravity of spatial triangles is given by using the judging conditions,so that students can have a deeper understanding and mastery of the center of gravity of spatial triangle,which rovide technical support for the application of spatial triangle in the field of engineering technology.