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马上就要到圆这一单元的教学了,闲暇时老师们在办公室里讨论圆的知识。于是,我随口说了一句:“那球体的截面一定是圆吗?”“不是,会有椭圆。”不知哪位老师随口应付着。“球体会有椭圆截面?”放学后我还在问自己。思来想去也没有找到把球体截面切成椭圆的办法,索性反向思维吧,先切一个圆形截面出来,如果这个截面可以变成椭圆而还在圆中成立也可以呀!1.一个圆形如果变成椭圆形,需要一组互相垂直的直径,其中一条直径不变,另一条直径拉伸或缩短。可是随着直径的拉伸或缩短球体也跟着变形了。2.有人会说可以让这个截面倾斜一下就好,可是前提第一条直径不变,如果让这个圆形截面以这个不动直径为轴转动,“截面”就会跑出球体,显然这就不是截面了。所以我确信球体的任何截面都是圆形,只不过穿过球心的截面面积最大罢了。无论在小学数学的教学中,还是在实际生活中,我们对球体的认识远远不如对圆柱体的认识。正是
Soon it is time to teach in the unit of circle, and in the free time teachers discuss round knowledge in the office. So, I casually said: “That the sphere of the cross-section must be a circle? ” “Is not, there will be an ellipse. ” I do not know which teacher casually deal with. “Sphere will have oval cross section? ” I still ask myself after school. Thought to go and did not find the ball cut into elliptical cross-section approach, simply reverse thinking it, first cut a circular cross-section, if the cross-section can be turned into an ellipse but also in the circle can also be set! If the circle becomes oval, you need a set of mutually perpendicular diameter, one of the same diameter, the other diameter stretch or shorten. But with the diameter of the stretch or shortening of the sphere followed by deformation. 2. Some people may say that this section can be tilted just fine, but the premise of the first diameter unchanged, if the circular cross-section of the fixed diameter of the axis of rotation, “section ” will run out of the ball, obviously This is not a cross section. So I’m sure that any cross section of the sphere is round, except that the cross-sectional area through the center of the sphere is the largest. Whether in the teaching of elementary mathematics or in real life, our knowledge of the sphere is far less than the understanding of the cylinder. Exactly