数形结合是解题中常用的思想方法,很多问题使用数形结合的方法都能迎刃而解,且解法简捷。数形结合的实质就是将抽象的数学语言与直观的图形结合起来,“数”是数量关系的体现,而“形”则是空间形式的体现。“数”和“形”常依一定的条件相互联系,抽象的数量关系常有形象与直观的几何意义,而直观的图形性质也常用数量关系加以精确的描述。在研究数量关系时,有时要借助于图形直观地去研究,而在研究图形时,又常借助于数量关系去探求。华罗庚教授曾精辟概述:“数缺形,少直观;形缺数,难入微”。具体地说,就是在解决问题时,根据问题的背景、数量关系、图形特征或使“数”的问题借助于“形”去观察,或将“形”的问题借助于“数”去思考,这种解决问题的思想,称为数形结合思想。 Combination of several forms is often used in problem-solving methods, many problems can be solved using the method of number and form, and the solution is simple. The essence of the combination of numbers is the combination of abstract mathematical language and intuitive graphics, “number” is the embodiment of quantity relationship, and “shape” is the embodiment of space. “Number ” and “Shape ” are often related to each other according to certain conditions. The abstract quantitative relationship often has the geometric meanings of image and intuition, while the intuitive graphic nature is often described by the quantitative relationship. In the study of quantitative relations, sometimes with the help of graphical intuitive to study, and in the study of graphics, often with the help of quantitative relationship to explore. Professor Hua Luogeng had incisive outline: “Lack of shape, less intuitive; lack of shape, difficult to micro ”. Specifically speaking, in the process of solving a problem, the problem of “” can be observed by means of “shape ” or the problem of “shape ” according to the background of the problem, the relation of numbers, the characteristic of the figure, “Number ” to think, this idea of ​​solving the problem, known as the number of forms with thought.