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求复杂几何体的体积问题一直是数学中的一个难点.如果所求几何体是柱、锥、台、球中的一种或与之相关的组合在一起的几何体,我们可利用公式解决.如果公式解决不了时,就需要另辟蹊径,这里从理论上介绍两条途径:中国的祖暅原理、西方的微积分.一、什么是祖暅原理南北朝时代南朝的数学家祖暅求球体积时,使用一个原理:“幂势既同,则积不容异”.“幂”是截面积,“势”是立体的高.意思是两个同高的立体,如在等高处的截面积恒相等,则体
The problem of finding the volume of a complex geometry has always been a dilemma in mathematics. If the geometry we are seeking is one of the columns, cones, tables, balls, or the geometry associated with it, we can use the formula to solve it. If the formula is solved In the past, there was a need to find another way here to introduce theoretically two ways: the principle of ancestors in China and the calculus in the West. What is the principle of the ancestors? When mathematicians and ancestors of Southern and Northern Dynasties, : “” Power “is the cross-sectional area, ” potential "is a three-dimensional high.It means two high three-dimensional, such as the cut-off at the height Constant area and so on, the body