共点线与共线点问题的探讨  

Talking about Common Point Line and Common Line Point Problem

作　　者：任琛琛[1] 侯雨宏 REN Chen-chen;HOU Yu-hong(College of Mathematics and Informatics, Jiangxi Normal University,Nanchang 330022,China)

机构地区：[1]江西师范大学数学与信息科学学院,江西南昌330022

出　　处：《南昌师范学院学报》2019年第6期1-6,共6页Journal of Nanchang Normal University

基　　金：江西省高等学校教学改革研究项目,编号:JXJG-17-2-30;江西师范大学教学改革研究项目,编号:JXSDJG16050。

摘　　要：共点线及共线点问题是立体几何中常见的问题,在初等几何和高等几何中均有涉及。初等几何中,主要应用有关直线、夹角等的方法去解决,方法多样而且易懂。在高等几何中,它的一个重要内容是研究图形在射影变换下的不变性和不变量,而同素性和结合性又是它的主要不变性质。文章介绍了多种初等几何和高等几何证明点共线及线共点问题的方法,并运用到具体例题中。Common point line and common line point are common problems in solid geometry,which are involved in elementary geometry and higher geometry.In elementary geometry,the methods of line and angle are mainly used to solve these problems.The methods are various and easy to understand.In higher geometry,one of the important cons to study the non-projective transformation of graphics.Variability and invariance,and homomorphism and associativity are its main invariant properties.This paper mainly introduces several methods of proving collinearity and collinearity of points in elementary geometry and higher geometry,and applies them to specific examples.

关 键 词：共点线 共线点 不变性 

分 类 号：O18[理学—数学]