笛沙格定理在初等几何中的应用.docx

天津师范大学
本科毕业论文(设计)
题目:笛沙格定理在初等几何中的应用
学院:数学科学学院
学生姓名:朱保军
学号:09505011
专业:数学与应用数学
年级:2009级
完成日期:2013年5月13日
指导教师:武猛
笛沙格定理在初等几何中的应用
摘要:,:两个对应三点形、透视轴、,,着重介绍其在几何作图、共线问题、共点问题、,还可轻易看出在初等几何中一些繁琐证明或难以得证的问题,,给初等几何中一些共线或共点问题带来简易之路.
关键词:透视轴;透视中心;笛沙格定理;共点问题;共线问题
The Application of the Desargues Theorem to Elementary Geometry
Abstract: The Desargues theorem is an important theorem on the projective plane. Many theorems are based on it, using it can also prove some collinear or concurrent problems in the elementary geometry. This thesis will grasp the Desargues theorem’s pith that there are two corresponding triangles, perspective axis, perspective centre. By the introduction of the Desargues theorem, showing the beauty of its picture. After that, we focus on the application to geometric drawing, collinear, concurrent, dynamic problems. Moreover, we can easily see some problems plex proof or hard-to-get proof in the elementary geometry, but they will be clear at a glance by the Desargues theorem. This thesis is bound to fully show the important role of the Desargues theorem in the elementary geometry. What’s more, it will simplify the way to the some problems of the collinear or concurrent in the elementary geometry.
Key words: perspective axis; perspective centre; Desargues theorem; concurrent;
collinear
目录
1 引言.................................................................(1)
2 笛沙格定理相关概念及其定理...........................................(2)
基本概念.........................................................(2)
笛沙格定理.......................................................(3)
笛沙格逆定理.....................................................(4)
推论.............................................................(5)
笛沙格构图.......................................................(6)
3 笛沙格定理在初等几何中的应用........................