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在高中代数(甲种本)第二册第二章的例题或习题中,出现凸n边形对角线条数的公式,平面内某些直线交点个数的公式,n个自然数的平方和公式等,对于这些公式,教材中均是要求用数学归纳法来证明的,但是,在教学中往往有人提出:这些结论如何得到的呢?人们觉得,难处并不在于证明这些命题的正确性,而在于如何探求到这些结论,本文目的仅在于对培养学生探究能力方面作些探讨。大家知道,现实生活中许多问题都可以看成是以自然数为自变量的函数。例如安排循环球赛的场数f(n)与球队数n的关系;多边形的对角线条数f(n)与边数n的关系等,在研究这
In the examples or exercises of the second chapter of the second volume of high school algebra (a type), there are formulas for the number of convex n-sided diagonal lines, the formula for the number of intersections of certain straight lines in the plane, and the formula of the sum of squares of n natural numbers. Etc. For these formulae, the textbooks all require the use of mathematical induction to prove, but in teaching it is often said: how do these conclusions come from? People think that the difficulty lies not in the correctness of these propositions, but The purpose of this article is to explore how to explore these conclusions. As we all know, many problems in real life can be seen as a function of natural numbers as independent variables. For example, to arrange the relationship between the number of field f(n) of the recirculating ball game and the number of teams n; the relationship between the number of diagonal lines of the polygon f(n) and the number of edges n.