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培养和训练学生灵活运用所学知识解决实际问题的能力是中学数学课外小组的重要任务之一。为此我们介绍一个解决实际问题的例子,以供选择数学课外活动小组活动内容时作参考。在有除尘或通风设备的工厂中常会遇到一些用铁皮作成的一节一节连接起来象牛角状的弯管(如图1)。若将弯管每隔一节都旋转180°时,弯管的每一节的轴线恰好成一条直线,原来的弯管成了一个圆台(如图2)。它是由一个大圆锥截去一个小圆锥而成的,若再补上截去的小圆锥(图2中上部的虚线处)即成原来的圆锥了。原来弯管上的每条接缝都变成了圆锥面与某一平面的交线,这些交线显然都是椭圆。圆锥面是由扇形(圆锥侧面展开图)作
The ability to train and train students to use their knowledge to solve practical problems is one of the important tasks of the extracurricular math team. To this end, we introduce an example to solve practical problems, for the selection of math activities of extracurricular activities for reference. In factories with dedusting or ventilation, there are often sections of metal that are joined together like horns (Figure 1). If the elbows are rotated 180 ° every other section, the axis of each section of the elbows is exactly a straight line, and the original elbows become a circular table (Figure 2). It consists of a large cone truncated a small cone made, and then add a small truncated cone (upper dotted line in Figure 2) that is the original cone. The original bend on each seam has become a conical surface and a certain line of intersection, these lines are clearly elliptical. Conical surface is made of fan (cone side expansion)