| 摘要: |
| 针对目前高考试题在解析几何题目的命制特点，提出从射影几何的高等数学观点下处理近年全国各地高考数学试题中的解析几何解答题的思路，发现试题命制的高等几何背景；利用极点和极线理论对中学解析几何的点、线关系进行高观点认知，借助极点、极线理论，如概念认知、配极原则等，加强解析几何问题中定点、定直线类问题的纵向探究.只有居高临下方能势如破竹地为中学教师在解析几何试题的命制和教学提供思路，为学生在处理类似问题时寻找破题的有力工具，引导教师平时注意挖掘高等数学在中学数学中的应用，思考高等数学在中学数学的指导意义. |
| 关键词: 解析几何 极点 极线 配极原则 试题背景 |
| DOI： |
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| Application and Research on Vertex and Polar Line Theory Based on Mapping Geometry |
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CHEN Fang yu， ZENG Chang tao
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| Abstract: |
| According to the characteristics of analytic geometry questions in college entrance examination question preparation， this paper proposes the idea using mapping geometry view to deal with analytic geometry problems in the mathematical questions in college entrance examinations in recent years， and finds higher geometry background of the questions by using vertex and polar line theory to understand the relation between point and line in analytic geometry of middle school， and by using vertex and polar line theory such as concept recognition， polar allocation principle and so on to enhance the study of fixed point and fixed line problems in analytic geometry. Only by using advanced theory， can middle school teachers have the ideas in the analytic geometry question preparation， can the students find the method to solve the problems， and can we find the application and guidance of higher mathematics to the teaching of middle schools. |
| Key words: analytic geometry vertex polar line polar allocation principle question preparationbackground |
