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对于一个好的数学问题,美国数学教育家G·波利亚有过一个比喻:“好问题同某种蘑菇有些相像,它们都是成堆地生长,找到一个以后,你应当在周围找一找,很可能附近就有好几个.”波利亚的比喻形象而生动地说明了数学问题之间存在着紧密联系,下面我们从一个例子出发,来探讨在解决了一个数学问题之后,如何去寻找和解决与之相关的其他数学问题,并从中发现这个问题背后所隐藏的某种规律,也就是说,当你幸运地采到第一朵蘑菇之后,如何去寻找周围更多的蘑菇.
For a good math problem, G. Polia, a math educator in the United States, has a metaphor: “Good problems are somewhat like mushrooms, and they all grow in heaps. Once you find one, you should find one There may well be several nearby locations. ”" Polya’s metaphor vividly illustrates the close relationship between mathematical problems. Let’s start with an example of how to solve a mathematical problem To find and solve other mathematical problems related to it, and find out some hidden rules behind this problem, that is, how to find more mushrooms around when you are lucky enough to pick the first mushroom.