英文摘要 |
This paper compares methods for calculating the volume of a particular type of wedge-shaped solid described in the Qin dynasty bamboo-slip manuscript Shu (數Numbers) , the Western Han dynasty bamboo-slip manuscript "Suanshu shu" (筭數書Book on Calculations), and the "Jiuzhang suanshu" (九章筭術Nine Chapters on Mathematical Procedures) , and identifies the relation between them. The text of Shu provides new evidence to support the opmion that four basic solids, the cuboid, "qiandu" (壍堵right triangular prism), "yangma" (陽馬right rectangular-based pyramid), and "bienao" (鱉腝tetrahedron with four right triangle faces) were used to determine solid volumes in the Qin and pre-Qin periods. Based on the above, this paper sets out a design that supplements the text in Shu to describe a mathematical method for finding the volume of a wedge. It reasons that the method for calculating the volume of the solid described on bamboo strip no. 0456 was found by mathematical derivation, and then attempts to reconstruct how the ancients obtained this method. Drawing on the concepts of evolution and genes from biology, this paper argues that the mathematical methods set out in the three sources have common characteristics and thus share the same origin. That common origin might have been transmitted and incorporated into an ancestor of the "Jiuzhang suanshu" that predates the other two documents. This paper also proposes a new understanding of how the methods for finding solid volumes were worked out and then transmitted throughout early China. |