The Nine Chapters on the Mathematical Art
Liu Hui's commentary on "The Nine Chapters on the Mathematical Art" is the earliest edition of the original text available. 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. 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. In his commentary, Liu Hui finds a more accurate estimation of pi using the method of exhaustion. The method involves creating successive polynomials within a circle so that eventually the area of a higher-order polygon will be identical to that of the circle. From this method, Liu Hui asserted that the value of pi is about 3.14. 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.