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数学的一个基本作用 ,“就是提供自然现象的合理结构 .…数学已经给互不关联的事实的干枯骨架注入了生命 ,使其成了有联系的有机体 .”(M .克莱因 ) .象本篇那样 ,虽然讨论的只是一个小课题 ,却使学生们看到了 ,数学内容之间的联系是那么紧密 ,数学事实的生命力是那样的强盛 ,它会延伸得很远很远 .也就是在这样的过程中 ,数学对象的本质自然地得到了揭示 ,数学的美 ,也明白地得到了昭示 :你看 ,球体积与球的表面积之间的关系 ,竞然也可以纳入到有内切球的几何体的体积公式之中 .可惜的是 ,流行的总是割裂地孤立地零碎地考题的现实 ,使这一种生动的发展式的在事物的联系中学的做法 ,很少能在课堂上见到了 .因此 ,可以顺便问一句 :联系 ,发展 ,结构 ,美 ,…也能进入考题中么 ?]
A fundamental role of mathematics, “is to provide a reasonable structure of natural phenomena....Mathematics has infused life into a dry skeleton of unconnected facts, making it an associated organism.” (M. Klein). In this article, although only a small topic was discussed, students were able to see that the connection between mathematical content was so tight and the vitality of mathematical facts was so powerful that it would extend far and far. In this process, the nature of the mathematical object has naturally been revealed. The beauty of mathematics has also been explicitly stated: You see, the relationship between the volume of the ball and the surface area of the ball can also be incorporated into the ball In the volume formula of the geometry, it is a pity that the popular practice of always isolated and fragmented examination questions makes this kind of vivid developmental method of middle school in the matter of seldom met in class. That’s it. So, by the way, you can ask: “Contact, development, structure, beauty, ... can you get into the exam?”