利用数形结合方法求解几类代数问题

Solving Several Kinds of Algebra Problems by Using the Number Shape Union Method

数学研究的对象是现实世界的数量关系(数)和空间形式(形)。“数”和“形”常按照一定的条件相互转化。数形结合思想是数学的重要的思想方法之一,并蕴于数学基础知识和基本技能之中,在数学解题中应用十分广泛。其实质是将抽象的数学语言与直观图形结合起来,发挥“数”与“形”两种信息的转化及其优势互补与整合,使逻辑思维与形象思维完美统一起来。对于培养学生的创新意识和创造思维具有积极的促进作用。

Mathematics research object is the relation between stoichionetric （number） and the spatial form （shape） in the real world. ＂The number＂ and ＂the shape＂ often transform mutually with a certain condition. The union of number and shape is one of important mathematics thinking methods, and contain in mathematics elementary knowledge and the basic skills, applying extensively in mathematics problem solving, whose essence is the combination of abstract mathematical linguistics and the visual picture, displaying the information transformation, superiority supplementary and conformity of ＂number＂ and ＂shape＂ to achieve the perfect unit of the logical thinking and the thinking in images. Therefore, such unit has the positive function in cultivating students＇ innovative ideology and thought.