简析数形结合在解题中的应用
 

摘要：数学是数与形的统一，用数形结合的思想方法研究问题，就是注意数与形两个方面的结合，或者借助于数的精确性来阐明形的某种属性，或者借助形的几何直观性来阐明数之间的某种关系.这就是说，当我们把数形结合当作数学思想方法来应用时，数与形两者之中，一个为手段，另一个为目的.若能掌握并灵活应用数形结合的思想方法，将会拓展我们解数学题的途径，使我们得到意想不到的收获.本论文将以各种典型题型为例，说明数形结合在解题中的应用以及数形结合思想对拓展学生思维的影响.
关键词：数形结合；思维；数学思想；创新 
The Analysis of the Union of Shape and Number in Solving Problem `s Application
Abstract: Mathematics is unification of the number and the shape, to research question with the method of the union of number and shape, it pays attention to the number and the shape two aspects union, either draws support to the number accuracy expounded shape some kind of attribute, either draws support from the shape the geometry direct-viewing shape to expound between number some kind of relations. This meant, when we treat as the union of number and shape method of thinking mathematics application, the number and the shape two in, is a method, another is a goal. If can grasp and the nimble application number shape union thinking method, will be able to develop our way that slave the math’s problem, It could enable us to obtain the unexpected harvest. The present paper take each kind of typical topic as an example and explained the unification of number and shape to develop the student thought in the problem solving application as well as the union number and shape thought the influence.
Keywords: the union of number and shape；Thought,；Mathematics thought； Innovation
 

目　　录
1 数形结合概况……………………………………………………………………2
1.1 数形结合思想的实质、地位………………………………………………2
1.2 数形结合在数学解题中应注意的问题……………………………………2
1.3 与数形结合有关的内容……………………………………………………3
2 数形结合的相关例题……………………………………………………………3
3 正确使用“数形结合”思想，注意可能出现的问题…………………………10
3.1 画图不准确，忽视考虑图形的整体性……………………………………10
3.2 图形选择不合理，以偏概全………………………………………………10
参考文献……………………………………………………………………………13
致谢…………………………………………………………………………………14