交比在欧氏几何中的应用  

Applications of cross ratio in Euclidean Geometry

作　　者：顾莹燕[1] 

机构地区：[1]苏州经贸职业技术学院,江苏苏州215009

出　　处：《中国西部科技》2009年第12期116-117,共2页Science and Technology of West China

摘　　要：本文介绍了射影几何中主要的不变量——交比的定义,以及交比、调和点列、调和直线等概念在欧氏几何中的具体形式及相关性质,在此基础上,通过具体的例子阐述了如何利用交比简单地解决一些复杂的欧氏几何问题。In this paper,we introduce the definition of cross ratio which is the main invariant of projective geometry,as well as the specific forms of definitions and properties related to cross ratio, harmonic range of points,harmonic pencil of lines in Euclidean geometry.On this basis,we give concrete examples of how to solve some complex problems in Euclidean geometry simply by using cross ratio.

关 键 词：交比 调和点列 射影几何 欧氏几何 

分 类 号：O184[理学—数学] O185.1[理学—基础数学]