Fangcheng (mathematics): Difference between revisions

'''Fangcheng''' (sometimes written as '''fang-cheng''' or '''fang cheng''') ({{zh|c=方程|p=fāng chéng}}) is the title of the eighth Chapterchapter of the [[Chinese mathematics|Chinese mathematical]] classic [[Jiuzhang suanshu]] (The Nine Chapters on the Mathematical Art) composed by several generations of scholars who flourished during the period from the 10th to the 2nd century BCE. This text is one of the earliest surviving mathematical texts from China. Several historians of Chinese mathematics have observed that the term ''fangcheng'' is not easy to translate exactly.<ref name="Hist01">{{cite book |author=Jean-Clause Martzloff |title=A History of Chinese Mathematics |date=2006 |publisher=Springer |page=250}}</ref><ref name="Hart01">{{cite book |author=Roger Hart |title=The Chinese Roots of Linear Algebra |date=2011 |publisher=The Johns Hopkins University Press |url=https://muse.jhu.edu/chapter/322683 |accessdate=6 December 2016}}</ref> However, as a first approximation it has been translated as "[[Matrix (mathematics)|rectangular arrays]]" or "square arrays".<ref name=Hist01/> The term is also used to refer to a particular procedure for solving a certain class of problems discussed in the Chapter 8 of The Nine Chapters book.<ref name=Hart01/>

The procedure referred to by the term ''fangcheng'' and explained in the eighth Chapterchapter of The Nine Chapters, is essentially a procedure to find the solution of systems of ''n'' equations in ''n'' unknowns and it is equivalent to certain similar procedures in modern [[linear algebra]]. The earliest recorded ''fangcheng'' procedure is similar to what we now call [[Gaussian elimination]].

The ''fangcheng'' procedure was popular in ancient China and it was transmitted to [[Japan]]. It is possible that this procedure was transmitted to [[Europe]] also and served as precursors of the modern theory of [[Matrix (mathematics)|matrices]], [[Gaussian elimination]], and [[determinant]]s.<ref name="Hart02"/> It is well known that there was not much work on linear algebra in [[Greece]] or [[Europe]] prior to [[Gottfried Leibniz]]’s studies of [[Elimination theory|elimination]] and determinants, beginning in 1678. Moreover Leibniz was a [[Sinophile]] and was interested in the translations of such Chinese texts as were available to him.<ref name="Hart02">{{cite book |author=Roger Hart|title=The Chinese Roots of Linear Algebra |date=2011 |publisher=The Johns Hopkins University Press |url=https://muse.jhu.edu/chapter/322679 |accessdate=6 December 2016}}</ref>