高等几何的群论观点对初等几何的指导作用

The Directive Functions of Group-theoretical viewpoint of Higher Geometry to Elementary Geometry

本文从仿射变换 ,仿射性质、仿射量 ,仿射对应图形入手 ,通过实例 ,分析、探讨高等几何的群论观点对于初等几何的指导作用 ,在较高层面上认识几何空间的基本特性、研究方法、内在联系、确认几何学的本质 ,以便更深入地认识和掌握初等几何 ,指导初等几何的教学与研究 ,居高临下地认识初等几何的内涵与外延。同时 ,进一步认识到高等几何不仅在提高观点方面具有独特作用 ,而且在论证方法 ,思考问题等方面具有独特的巧妙。

This article begins with the following terminologies;affine transformation, affinity, affine quantity, affine corresponding figures, analyzing and researching. By some examples,the directive functions of group theoretical viewpoint of higher geometry to elementary geometry.The basic characteristics,researching methods and the internal relations of geometric space can be understood in higher level. Furthermore,the essence of geomtry will be recognized.This article is benefical to the deeper study and mastery of elementary geometry, the directions to elementary teaching and researching, the knowledge of the connotation and extention of elementary geometry. At the Same time, such further conclusions can be reached as the unique functions in improving certain viewpoints and the cleverness and flexibility in thinking about problems and demonstrating methods.