论文部分内容阅读
八二年天津市初中升学考试数学试题第八题是:“已知半圆O中内接梯形ABCD,下底AB=2R,求梯形ABCD周长的最大值。”该题实质上是求二次函数的最大值问题。解这种题目,初中学生往往是感到比较困难的。究其原因,所在多有,主要的有二;一是平时学习中往往不大注意平面几何中的“最值”问题;二是不会将平面几何的问题转化为代数问题进行求解。因而,在初中平面几何教学中,重视“最值”问题的教学,并引导学生学会解决这类问题的方法无疑是必要的。其实,平面几何中有不少公理、定理都涉及到“最值”。例如,在连接两点的线中,线段最短;连接直线外一点和直线上各点所得到的线段中,以和直线垂直的线段为最短;直径是圆内最大的弦;等
The eighth question of the mathematics test for the Tianjin junior high school entrance examination in 1982 was: “The semicircle O is known to have a trapezoidal ABCD and a lower base AB=2R. The maximum length of the ABCD perimeter of the trapezoid is to be found.” The problem of the maximum value of the function. To solve this problem, junior high school students often feel more difficult. There are many reasons for this, and there are two major ones. One is that in peacetime learning, the “maximum value” problem in plane geometry is often not paid attention; second, the problems of plane geometry are not transformed into algebraic problems. Therefore, in the teaching of plane geometry in junior middle school, it is necessary to attach importance to the teaching of “the most value” problem and guide students to learn how to solve such problems. In fact, there are many axioms and theorems in plane geometry that involve the “most value.” For example, in a line connecting two points, the line segment is the shortest; in a line segment connecting a point outside the line and each point on the line, the line segment perpendicular to the line is the shortest; the diameter is the largest string within the circle; etc.