蝴蝶定理对合对应关系的统一形式及其应用  

The Unified Form of the Corresponding Relation of Butterfly Theorem and Its Application

作　　者：赵临龙 朱亮卫 于婷 ZHAO Linlong;ZHU Liangwei;YU Ting(School of Mathematics and Statistics,Ankang University,Ankang 725000,Shaanxi China;School of Mathematics and Computer Science,Shaanxi University of Technology,Hanzhong 723000,Shaanxi China)

机构地区：[1]安康学院数学与统计学院,陕西安康725000 [2]陕西理工大学数学与计算机科学学院,陕西汉中723000

出　　处：《河南科学》2020年第5期689-693,共5页Henan Science

基　　金：陕西省“高层次人才特殊支持计划”项目(2019TZJH01);安康学院硕士点培育学科专项(2016AYXNZX009)。

摘　　要：利用射影几何的对合关系式,给出二次曲线统一的蝴蝶定理推广形式,同时指出相关文献中的蝴蝶定理推广形式的问题,并且利用该推广结论,解决欧式几何中的问题.By using the involutive relation of projective geometry,the generalized form of unified butterfly theorem for quadratic curve is given.At the same time the wrong conclusion of the extended form of butterfly theorem in related literature is pointed out,and the problems in Euclidean geometry are solved by using this conclusion.

关 键 词：蝴蝶定理 二次曲线 射影几何 对合关系 统一形式 

分 类 号：O182.1[理学—数学]