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七年级数学《整式的加减》中有这样一道探究题:如图1所示,用若干火柴棒拼成一排由三角形组成的图形,如果图形中有2,3或4个三角形时,分别需要多少根火柴棒?如果图形中有n(n≥2)个三角形,需要多少根火柴棒?本文就图形中有n(n≥2)个三角形进行发散思维,以求深刻理解这类问题的本质.一、总结数字规律,得出结论在上列表格中,由三角形的个数与火柴棒根数的规律比较发现:三角形的个数从1增加到n(n≥2)时,火柴棒的根数是从3开始的奇数间隔增加的,即三角形每增加一个,火柴棒的根数就增加2.这样,就不难发现,当有n(n≥2)个三角形时,火柴棒的根数是2n+1(n≥2).
The seventh grade mathematics, “the whole addition and subtraction,” there is such a research topic: as shown in Figure 1, with a number of match sticks spell into a row of graphics composed of triangles, graphics, if there are two or three triangles, respectively, How many matchsticks? If there are n (n≥2) triangles in the graph, how many matchsticks are needed? In this paper, there are n (n≥2) triangles in the graph divergent thinking in order to deeply understand the nature of such problems First, summarize the law of the number, concluded that in the above table, the number of triangles and the number of matchstick rod law found that: the number of triangles increased from 1 to n (n ≥ 2), matchstick The number of roots is increased from the odd interval starting from 3, that is, the number of match sticks increases for every increment of the triangle 2. Thus, it is not difficult to find that when there are n (n≥2) triangles, the root of match sticks The number is 2n + 1 (n ≧ 2).