例谈高等几何观念下对平面几何问题的审视

对一道平面几何竞赛题运用初等方法给出证明后,通过运用解析法、射影几何方法的证明,可以将其推广到三角形与二阶曲线相切的情形。由此更深层次地透视出高等几何观念下几何图形的性质。

Case-based Review of the Problems of the Plane Geometry Under High-Concept

After proofs of a plane geometry contest problem are given by using primary methods,the case could be extended to the situation of the triangle and the second tangent through the use of analytical method,projective geometry method.From this perspective the nature of geometry could be reviewed to a deeper level under the framework of high-concept.