浅谈蝴蝶定理的再推广及其应用

Further generalization and application of the butterfly theorem

本文以高等几何的相关理论为背景,充分利用射影几何的交比,从二次曲线定弦BC上的任意一点、二次曲线内或外的任意一定点A、正方形、变态的二次曲线等四个方面对蝴蝶定理进行了再推广,并给出推广后命题的一些简单应用。

This paper generalizes the butterfly theorem again from four aspects under the back- ground of higher geometry theory and using the intersection ratio of the projection geometry. That is an arbitrary point of the fixed chord BC of the conic section, an arbitrary point in or out of the conic section, square and abnormal conic. And then studies some simple applications of the generalized propositions.