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本论文旨在探究向量方法在中学数学中的典型应用。开篇首先概述了向量这一内容引入中学数学教材的内涵与外延,同时以用向量方法求三角形的面积为例指出了向量在几何中的广泛应用。其次,介绍了构造向量求无理多项式最值的方法,以及得出了向量列的一系列概念,为进一步深入探究向量奠定了基础。最后,探讨了从不同的角度出发,运用多种向量方法求解同一个数学问题,这样使问题分析得更透彻,思维也更开阔,充分展现了数学的创造美。
The purpose of this thesis is to explore the typical application of vector method in middle school mathematics. First of all, the introduction begins with the introduction of vector to introduce the connotation and denotation of high school math textbooks. At the same time, we use the vector method to find the area of the triangle as an example to show that the vector is widely used in geometry. Secondly, we introduce the method to find the most value of the irrational polynomial and find out a series of concepts of vector column, which lays the foundation for further exploration of vector. Finally, it discusses how to solve the same mathematical problem from different perspectives by using a variety of vector methods, so that the problem can be analyzed more thoroughly and the thinking can be broadened, which fully demonstrates the creation beauty of mathematics.