Liu Hui

Surveying

Liu Hui also presented, in a separate appendix of 263 AD called Haidao Suanjing or The Sea Island Mathematical Manual, several problems related to surveying. This book contained many practical problems of geometry, including the measurement of the heights of Chinese pagoda towers. This smaller work outlined instructions on how to measure distances and heights with "tall surveyor's poles and horizontal bars fixed at right angles to them". With this, the following cases are considered in his work:

The measurement of the height of an island opposed to its sea level and viewed from the sea The height of a tree on a hill The size of a city wall viewed at a long distance The depth of a ravine (using hence-forward cross-bars) The height of a tower on a plain seen from a hill The breadth of a river-mouth seen from a distance on land The width of a valley seen from a cliff The depth of a transparent pool The width of a river as seen from a hill The size of a city seen from a mountain.

Liu Hui's information about surveying was known to his contemporaries as well. The cartographer and state minister Pei Xiu (224–271) outlined the advancements of cartography, surveying, and mathematics up until his time. This included the first use of a rectangular grid and graduated scale for accurate measurement of distances on representative terrain maps. Liu Hui provided commentary on the Nine Chapter's problems involving building canal and river dykes, giving results for total amount of materials used, the amount of labor needed, the amount of time needed for construction, etc.

Although translated into English long beforehand, Liu's work was translated into French by Guo Shuchun, a professor from the Chinese Academy of Sciences, who began in 1985 and took twenty years to complete his translation.