数形结合在解题中的应用.doc

摘要：数形结合是数学中重要的思想方法。它不仅是一种重要的解题技巧，也是一种重要的数学思维方法。几何图形的形象直观，便于理解，代数方法的一般性，解题过程的机械化，可操作性强，便于把握。本文在概述数形结合思想方法的基础上，对其在数学解题中的应用作一探讨，并主要从以下几个方面进行了讨论：（1）数形结合在概率中的应用。（2）数形结合在圆锥曲线中的应用。（3）数形结合在不等式中的应用。

[关键词] 数学思想; 数形结合; 概率; 不等式; 圆锥曲线。

[Abstract] Several form combining is an important way of thinking in mathematics. It is not an important problem solving skills, also is a kind of important mathematics thought method. Geometry image intuitive, easy to understand, the general algebraic method, the problem solving process of mechanization, the maneuverability is strong, easy to grasp. Method based on an overview of the number form combining ideas, on the basis of the paper in the application of mathematical problem solving, and mainly from the following several aspects are discussed.(1) the number form combining in the application of the probability.(2) the number form combining with its application in conic section.(3) the number form combining in the application of inequality.

[Key Words] mathematical ideology; combination of quantities and spatial forms; the probability; inequality; conic section.

目录

前言

1. 数形结合思想方法概述

1.1 数形结合思想方法

1.1.1以“数”化“形”

1.1.2以“形”变“数”

1.1.3“形”“数”互变

1.2数形结合思想方法的价值

2. 数形结合在解题中的应用

2.1 数形结合在概率中的应用

2.1.1 形数互变

2.1.2 以形助数

2.2 数形结合在圆锥曲线中的应用

2.2.1 以形助数

2.2.2 以数助形

2.3 数形结合在不等式中的应用

2.3.1 以形助数

2.3.2 以数助形

3. 总结

参考文献：

致谢