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    National Tsing Hua University Institutional Repository > 清華出版品 > 01 清華學報 > 新27卷第2期 >  再論劉徽關於陽馬與羨除公式的證明

    Please use this identifier to cite or link to this item: http://nthur.lib.nthu.edu.tw/dspace/handle/987654321/75683

    Title: 再論劉徽關於陽馬與羨除公式的證明
    Other Titles: On Ancient Chinese Derivation of the Volumes of A Pyramid and A Cuneate Solid
    Authors: 屈安京;An-jing Qu
    Date: 1997/06
    Publisher: 國立清華大學出版社
    Relation: 清華學報,國立清華大學,1997,new,27,n.2,p201.
    Keywords: 羨除公式
    Abstract: The theory of polyhedron volume in ancient Chinese mathematics was based on yangma shu, the volume of a pyramid. Yanchu 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 than the understanding of those who divided a yanchu into many cases, and then found that some cases Liu Hui did not give proofs. The reasult is that Liu Hui's proof on yanchu shu is complete.
    Key Words: Liu Hui, volume of pyramid, volume of cuneate solid, polyhedron
    URI: http://thjcs.hss.nthu.edu.tw/catalogue_detail.php?id=176
    Appears in Collections:[01 清華學報] 新27卷第2期

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