二次曲线数例研讨的射影几何学方法  

Projective Geometry Method in the Framework of Quadratic Curve

作　　者：宋占奎[1] 

机构地区：[1]湖北十堰职业技术学院公共课部,湖北十堰442000

出　　处：《西安文理学院学报（自然科学版）》2012年第1期78-81,共4页Journal of Xi’an University(Natural Science Edition)

摘　　要：用射影几何的概念法探讨了二次曲线数例的射影性质.得到了变动三角形第三顶点的轨迹;平面上给定其中无三点共线的四点A,B,C,D,满足P(AB,CD)为常数的点P的轨迹;给定二次曲线上五点求作曲线上另外一些点;给定二次曲线五条切线,求作曲线另外一些切线;求作二次曲线上五点之一的切线;证得了六边形内接于一二次曲线;三点共线;三线共点以及共轭点偶的对合对应.We make a discussion of the projective properties of quadratic curve by using conceptual model of projective geometry.As a result,the third apex＇s locus of an alterable triangle is offered.There are four points A,B,C and D in a plane and any three points are not collinear.They satisfy the qualification that the locus of the point P（AB,CD） is constant.Five points in a quadratic curve are offered,other points in the quadratic curve are to be sought for.Five tangents of the quadratic curve are offered,other tangents of it are to be sought for,and so are these five points＇ tangents.It is proved that the hexagon is inscribed in the quadratic curve.The three points are collinear.The three lines are concurrent.The conjugated pair is convoluted and correspondent.The locus as mentioned before is proved to a quadratic curve.Other points in the curve and the tangents of the curve are obtained,so are the points＇ collineation,the lines＇ concurrence and the convolution and correspondence of the conjugated pair.

关 键 词：点列 线束 极点 共轭点偶 对合对应 Pascal线 Brianchon.点 

分 类 号：O185.1[理学—数学]