不等式的几何证法中应注意的两个问题

• 作 者: 李长明
• 机 构: 贵州教育学院数学系,
• 出 处: 中等数学
• 发表日期: 1986年04期
• 关键词: 证法 数学竞赛 繁简 几何方法 图形的 直角坐标系 余弦函数 开区间 相互位置关系 单位正方形

(一)图形的选择与证法的优劣许多不等式常可运用几何方法去证。几何证法的优点是:抽象的量被赋予了直观的几何形象,因而孰大孰小易于判明。然而几何图形的选择是否得当,不但有繁简之别,而且说服力也大有差异,甚至还会影响到结论适用的范围,试看如下数例。先看1982年苏联中学生数学竞赛中的一

(a) the choice of graphics and the pros and cons of the testimony Many inequalities can often be verified using geometric methods. The advantage of geometrical proving is that the amount of abstraction is given an intuitive geometrical image, so it is easy to identify large and small. However, whether or not the choice of geometrical figures is appropriate is not only a matter of simplification, but also a difference in persuasiveness. It will even affect the scope of the conclusions. Take a look at the following examples. Look at one of the 1982 Soviet high school mathematics competitions