Historical and mathematical texts show that fairly advanced mathematical methods were involved in the planning of public works in ancient China. It would seem that the actual design of earthworks and canals was done locally, by persons familiar with the topography, and therefore is difficult to see in the historical record, which generally focuses on the Imperial court. However the organization of the necessary labour force for very large projects was done by higher officials, often at the court level, and this we know more about. The necessary calculations included the volumes of earth to be moved, the volume production norms for groups of labourers, and the dimensions of parts of constructions to be completed by particular groups. This last often involved what in modern terminology would be called the formulation and numerical solution of quadratic and cubic equations.

An example is in the mathematical section of the 14th-century book on river conservancy Hefang tongyi. The dimensions and volume of a planned canal, to be dug by several groups of labourers from different counties, are given. One of the groups, with a given volume production norm, starts digging at one end of the canal, and the distance they are to dig is to be calculated. The answer is a root of the equation 15x^2+94500x=11556000. (See staff.hum.ku.dk/dbwagner/another.htm.)

An unexpected fact which emerges from this study is that in ancient China public works planning was very often done by astronomers. A question I wish to ask at the Symposium is whether this phenomenon is seen in other ancient cultures.

For the full presentation of this contribution, see:

http://www.staff.hum.ku.dk/dbwagner/SAW/SAW.html