The Chinese concept of Cavalieri's principle and its applications

Abstract

Bonaventura Cavalieri (1598–1647) was noted for his method of indivisibles which led to the principle which bears his name. In the third century, while attempting to derive the volume of a sphere, Liu Hui applied a similar principle to determine the ratio of the volumes of a sphere and a solid circumscribing the sphere. This solid is formed by the intersection of two perpendicular cylinders circumscribing the sphere and is called mou he fang gai. Liu Hui left unresolved the problem of finding the volume of the mou he fang gai. In the fifth century Zu Geng, also applying Cavalieri's principle, solved this problem and thus derived the volume of a sphere. The influence of Zu Geng's method on later mathematicians is discussed in the latter part of the article.