节点文献

内接于二阶曲线的完全六点形对边点共线的充要条件

The Sufficient and Essential Condition of Collinearity of Diagonal Points of a Complete Six-Point Shape Inscribed in the Curve of Second Order

  • 推荐 CAJ下载
  • PDF下载
  • 不支持迅雷等下载工具,请取消加速工具后下载。

【作者】 杨海玲; 杨晨曦;

【Author】 YANG Hai-ling1 YANG Chen-xi2(1.Yimen No.1 Middle School,Yimen,Yunnan 651100;2.Department of Mathematics,Yuxi Teachers College,Yuxi,Yunnan 653100)

【机构】 易门一中; 玉溪师范学院数学系 云南易门651100; 云南玉溪653100;

【摘要】 在Pascal定理中,若二阶曲线退化为两条直线时,Pascal定理就变为Pappus定理.同样地,若定理“对于任意一个内接于非退化二阶曲线的完全六点形,它的6对对边的交点共线的充要条件是3对对顶点的连线共点”中的二阶曲线也退化为两条直线时,此定理就变为另一定理——“Pappus线过两底交点的充要条件是两点列对应点的连线共点”.

【Abstract】 Pascal theorem turns into Pappus theorem when the curve of second order is degenerated into two straight lines.Similarly,in the theorem of "for any complete six-point shape inscribed in the curve of second order,the intersection points of its six pairs of opposite sides become collinear if and only if the connecting lines of the three pairs of opposite vertexes are concurrent",if the curve of second order is degenerated into two straight lines,then this theorem turns into another theorem-"the Pappus line passes through the intersection point of two bottom sides if and only if the connecting lines of the corresponding points of two tiers are concurrent."

  • 【文献出处】 玉溪师范学院学报 ,Journal of Yuxi Teachers’ College , 编辑部邮箱 ,2007年03期
  • 【分类号】O185
  • 【下载频次】60
节点文献中: 

本文链接的文献网络图示:

本文的引文网络