高等几何命题对初等几何的指导作用探讨

通过实例，分析，探讨高等几何命题对于初等几何的高观点指导作用。在更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，从而发展几何空间的概念，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，灵活等特点。

Research on the Directive Functions of Higher Geometry Assignments to Elementary Geometry

The driective functions of higher geometry assignments to elementary geometry can be acquired by analyzing and probing into the examples in higher geometry.The basic characteristics,researching methods and the internal relations of geometric space can be understood from higher level.Furthermore.the essence of geometry will be recognized.As a sesult,the concept of geometric space is developed,which is beneficial to the deeper knowlege and mastery of elementary geometry,the directions to elementary geornetry teaching and researching,and the knowlege 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 questions and demonstrating methods.