Title

On Ancient Chinese derivation of the Volumes of A Pyramid and A Cuneate Solid

Author

Qu Anjing

Genre

Article  

Pages

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Language

Key words

Liu Hui, volume of pyramid, volume of cuneate solid, polyhedron

Abstract

      The theory of polyhedron volume in ancient Chinese mathematics was based on yangma shu, the volume of a pyramid. Ynachu shu, the volume of a cuneate solid, did not exist in Euclid’s Elements. The derivation of yangma shu and yanchu shu in Liu Hui’s commentary on the Nine Chapters on Mathematical Art has been studied by scholars in and out China. In order to understanding the meaning of yangma shu, several key words in orinial text have been changed in different ways. In fact, only one word was misprinted in Liu Hui’s commentary on yangma shu. It has been considered that the proof of yanchu shu in Liu Hui’s commentary is not perfect. The reexamination on yanchu shu shows that Liu Hui’s proof is much concise tthan the understanding of those who divided a yanchu into many cases, and then found that some cases Liu Hui did not give proofs. The result is that Liu Hui’s proof on yanchu shu is complete.