论文部分内容阅读
所谓特殊化,是将一般问题的研究转化为特殊情形,通过特殊情形的解决而去探索一般规律,寻找解决一般问题的途径或者否定已有的猜想。这是解决数学问题的一个重要思想方法。下面举一些例子,说明在特殊化的思想指导下所显示的一些成效。一揭示事物的规律从人们认识事物运动的规律来说,总是由认识个别的和特殊的事物逐步扩大到认识一般事物的,从许多特殊事物中,概括出它们共同的本质。例1 观察凸多面体的面数、顶点数、棱数,寻找它们之间的关系:
The so-called specialization is to turn the research of general issues into special situations, to explore general laws through the solution of special situations, to find ways to solve common problems or to reject existing conjectures. This is an important way of thinking to solve math problems. Here are some examples of some of the achievements shown under the guidance of specialization. A law that reveals things from the laws of people’s understanding of the movement of things, from the understanding of individual and special things gradually to the understanding of general things, from many special things, summed up their common essence. Example 1 Observe the number of faces, vertices, and number of edges of a convex polyhedron and find the relationship between them: