Research On The Problem Solving Of Plane Geometry In Competition Mathematics By Triangulation Method

Trigonometry is a kind of algebraic method and an important mathematical thought method.Using trigonometric method to study geometric competition problems can usually make the relationship between the variables in the problem simple and clear,reason clearer,reasoning simpler,methods sharper,and not only have more time and energy to learn mathematics well.It can also achieve better results in exams and competitions.However,the research on trigonometric method for teaching in competitive mathematics is very rare at present.Based on this phenomenon and combined with its own study and classroom teaching practice,this paper puts forward the subject.In this paper,the mathematical theory,basic knowledge,formula theorem and geometric question type involved in trigonometric method are discussed.This paper focuses on the teaching value of trigonometric method in competition mathematics and the application value of solving problems.There are three main aspects of the research,one is trigonometric method in plane geometry,the other is the research of trigonometric method in plane geometry,and the third is the application of trigonometric method in the teaching of solving problems.This paper first analyzes the research history and presentsituation of triangular method at home and abroad,Zhang Jingzhong academician's educational mathematics thought and the relation between Polya's problem solving theory and trigonometric method,which is the theoretical foundation of trigonometric method.Then starting with trigonometric knowledge and trigonometric theorem,this paper studies the concrete implementation of trigonometric method for solving geometric problems in competition mathematics,and focuses on the analysis of "how to find a suitable triangular method" and "why so".Then,starting from different geometric problems,this paper expounds in detail how to select the appropriate trigonometric method to solve the problem according to the characteristics of the relation between the conditions or the conclusion in the problem.The fifth chapter of this paper is the teaching design of using trigonometric method to solve geometric problems of mathematics contest in junior middle school and senior high school.Through the inspiration and guidance of examples,students can learn to use trigonometric method.Finally,some five-point teaching suggestions are put forward to solve theproblem with trigonometric method.