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数形结合就是把抽象的数学语言与直观的图形结合起来,通过数与形之间的对应和转化来解决数学问题,它包含“以形助数”和“以数解形”两个方面.利用它可使复杂问题简单化、抽象问题具体化,它兼有数的严谨与形的直观之长,是优化解题过程的重要途径之一,是一种基本的数学方法.一、利用数形结合思想解决集合的问题1.利用韦恩图法解决集合之间的关系问题一般用圆来表示集合,两圆相交则表示两个集合有公共元素,两圆相离则表示两个集合没有公共元素.若利用韦恩图法则能直观地解答有关集合之间的关系的问题.例如:
The combination of numbers is the combination of abstract mathematical language and intuitive graphics to solve mathematical problems through the correspondence and conversion between numbers and forms. Two aspects.Using it to make the complex problem simple and the abstract problem concrete, it combines the number of rigorous and the shape of the intuitive long, is an important way to optimize the process of solving one of the basic mathematical method is a , Using the combination of ideas to solve the problem of the collection 1. The use of Wayne diagram to solve the relationship between the collection The problem is generally represented by a circle, the two circles intersect said two sets have public elements, the two circles away from that two There are no common elements in a set, and the Wayne diagram can intuitively answer questions about the relationship between the sets. For example: