Editing Chinese mathematics (section)

=== Liu Hui's commentary on ''The Nine Chapters on the Mathematical Art'' ===
[[File:Liuhui geyuanshu.svg|thumb|Liu Hui's exhaustion method]]
[[Liu Hui]]'s commentary on ''The Nine Chapters on the Mathematical Art'' is the earliest edition of the original text available.{{sfn|Dauben|2013}} Hui is believed by most to be a mathematician shortly after the Han dynasty. Within his commentary, Hui qualified and proved some of the problems from either an algebraic or geometrical standpoint.{{sfn|Siu|1993}} For instance, throughout ''The Nine Chapters on the Mathematical Art'', the value of pi is taken to be equal to three in problems regarding circles or spheres.<ref name=":82" /> In his commentary, Liu Hui [[Liu Hui's π algorithm|finds a more accurate estimation of pi]] using the [[method of exhaustion]].<ref name=":82" /> The method involves creating successive polygons within a circle so that eventually the area of a higher-order polygon will be identical to that of the circle.<ref name=":82" /> From this method, Liu Hui asserted that the value of pi is about 3.14.{{sfn|Needham|1959}} Liu Hui also presented a geometric proof of square and cubed root extraction similar to the Greek method, which involved cutting a square or cube in any line or section and determining the square root through symmetry of the remaining rectangles.<ref name=":92" />