The Chinese concept of Cavalieri's principle and its applications
type: Item
instance of: scholarly article
title: The Chinese concept of Cavalieri's principle and its applications
zbMATH Open document ID: 0592.01004
DOI: 10.1016/0315-0860(85)90020-5
author: Lay-Yong Lam
author: Kangsheng Shen
published in: Historia Mathematica
publication date: 1985-01-01T00:00:00Z
review text: Put in modern language of calculus, that the volume of solid is \(\int^{b}_{a}A(x)dx\) is called Cavalieri principle. In the third century, while attempting to derive the volume of a sphere, Liu Hui applied a similar principle to determine the ratio of a sphere and a solid circumscribing the sphere. The 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. This shows that the principle was known and applied over a mellenium before Cavalieri. A discussion on Mei Wending's and Xu Youren's work on areas and volumes shows that while Mei's work was stated mostly without proof and was influenced by a transmission from the West, Xu's work was a continuation of Zu's tradition.
Mathematics Subject Classification ID: 01A25
Mathematics Subject Classification ID: 28-03
zbMATH DE Number: 3950442
zbMATH Keywords: Cavalieri principle
zbMATH Keywords: Liu Hui
zbMATH Keywords: Zu Geng
zbMATH Keywords: Mei Wending
zbMATH Keywords: Xu Youren
zbMATH Keywords: volume of sphere
zbMATH Keywords: mou he fang gai
MaRDI profile type: Publication
full work available at URL: 0315-0860(85)90020-5
OpenAlex ID: W1967062328
cites work: Q5824330
cites work: An Old Chinese Way of Finding the Volume of a Sphere
cites work: Right-angled triangles in ancient China
cites work: Q3280103
description: scientific article; zbMATH DE number 3950442