一个小球,或者说所谓质点,从一个A点的位置开始,在只考虑重力作用下,沿怎样的一条路径下滑,可以以最短时间滑到比较低的一个B点位置? 这就是所谓最速降线问题。最速降线问题直接导致一次历史上最为牛人云集的数学竞赛,参赛者有牛顿,莱布尼茨,伯努利兄弟等人。“河中取物”问题示意图 (请将“空气”视作陆地,“水”视作河流即可):由半径为2的圆所生成的摆线示意图:
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