浅谈构造法在证明不等式中的应用.rar

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摘 要:构造法作为一种重要的化归手段,是数学中一种富有创造性的思维方法,在证明不等式中有着重要的作用,也在近些年的高考中体现了这方面的要求。文章采取了归纳总结的方法,通过构造几种数学模型:即:函数模型、几何图形模型、数列模型、方程模型、向量模型、三角函数模型、复数模型。以数学中某些典型为例,探讨了构造法在证明不等式中的应用,最后在总结中提及了构造法在中学数学中的教学价值和以后的努力方向。

关键词:构造法;模型;不等式

 

Abstract: As an important way of reduction, the constructive method can be creatively used in the study of mathematics. The importance is particularly evident in proving inequality,which has been one of the requirements in the entrance examinations in recent years. This paper focuses on the application of the constructive method in proving inequality with the method of induction and summary by using some mathematical models with typical examples such as functional model, geometric figure model, sequence of number model, equation model, vector model, trigonometric function model, and complex number model.  The paper concludes by discussing the value of the constructive method in mathematics teaching in the high school and its future development. 

Key words: constructive method; model; inequality

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