Fangcheng (mathematics)

rdf:langString Fangcheng (mathematics)

rdf:langString 方程

rdf:langString fāng chéng

rdf:langString Fangcheng (sometimes written as fang-cheng or fang cheng) (Chinese: 方程; pinyin: fāng chéng) is the title of the eighth chapter of the 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 BC. 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. However, as a first approximation it has been translated as "rectangular arrays" or "square arrays". The term is also used to refer to a particular procedure for solving a certain class of problems discussed in Chapter 8 of The Nine Chapters book. The procedure referred to by the term fangcheng and explained in the eighth chapter of The Nine Chapters, is essentially a procedure to find the solution of systems of n equations in n unknowns and 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 was transmitted to Japan. It is possible that this procedure was transmitted to Europe also and served as precursors of the modern theory of matrices, Gaussian elimination, and determinants. 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 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.