摘要
研究射影变换下的蝴蝶定理并加以证明.改变射影平面上蝴蝶定理中相应弦所在直线的位置、去掉条件"M为弦PQ中点"、考虑退化的二阶曲线等情形,得到在射影平面上蝴蝶定理的若干推论.在欧氏平面上运用类比法,得出蝴蝶定理在初等几何中的若干推论,并给出简洁证明.
It is studied and proved in this paper the version of butterfly theorem under projective transformation. We obtain some corollaries of it by transforming the position of bowstring, deleting the condition ＂M is the middle point of PQ＂, considering degenerate curves with second degree and some other cases. Also we obtain some corollaries of butterfly theorem in elementary geometry and give their brief proofs by making use of the method of analogy on the Euclid plane.
出处
《阜阳师范学院学报（自然科学版）》
2009年第4期33-38,共6页
Journal of Fuyang Normal University(Natural Science)
基金
校级重点科研项目(2008-ASL-09)资助
关键词
蝴蝶定理
射影变换
二阶曲线
butterfly theorem
projective transformations
curves of second degree
