这是一个有趣、颇具启发性的话题.一次自己在教学中这么问学生:“一个半球面状的酒杯,内部半径为R,放入一个半径不大于R的球,毫无疑问,球可坠到杯底.但若取一个内部为某圆锥曲线(抛物线、椭圆、双曲线)施转面的酒杯,杯口足够大,小球何以能坠底?”,学生们议论纷纷,但一时无以对 This is an interesting and inspiring topic. Oneself asked the students in teaching: “A hemisphere-shaped wine glass with an inner radius of R. Put a ball with a radius no greater than R. There is no doubt that the ball can fall. To the bottom of the cup. But if you take a wine glass with a conical curve (parabola, ellipse, hyperbola) on the inside, the cup is large enough so that the ball can fall to the bottom?”, the students talked about it, but there was no time Correct