The Cartographic Technology And Relative Scientific Thought Of Topographic Map In The Tombs Of The Han Dynasty At Mawangdui

ONE of the three maps is a topographic map. On the map, we can find that the location, orientation and the contour of the mountains have been presented by using the loop-line which is very similar to the orthomorphic projection. Particularly, the range of Jiu Yishan, a famous divine mountain in the ancient China, has been shown by the relative thicker contour lines and the characters of ridges of peaks have been described as the scale (scale on the fish) -like drawings. In addition, there are nine rectangular bars signs towards south and seven towards the east on the map. We suppose that these bars represent the number of major peaks of the mountain from the different viewpoints. Besides, the map shows some rivers detailedly, exactly and vividly as well.Archaeologists were impressed and puzzled by this map dated 2100 years ago because the level of mapping technology used in this map are comparable to modern maps, which are manifested by the high precision achieved in the mapping of rivers, and the representation of mountains and their peaks using conformal projection.Most available ancient Chinese maps were not based on field survey but were compiled indoor using direct or indirect travel and exploration records. The map preparation process can be roughly divided into the following steps. Firstly, the position of a geographical object is marked on the sketch map using its orientation and distance. The orientation data is based on the 8-orientation system in which the circumference is divided into 8 parts. The distance data is mainly based on the Chinese distance unit "Li", but a smaller unit "Bu" will be used for detailed description. Secondly, the rectification by "intersection" method is carried out in order to minimize the errors in the relative positions of a geographical object caused by the intrinsic "roughness" of the aforementioned spatial model. This "intersection" rectification method, which is similar to the "forward intersection" in modern surveytechnology, was analyzed in this article from three angles: (1) the simulation study of the 2nd century B.C. survey map "Mawang Dui Map", (2) the analysis of the traditional survey theory recorded in Zhou Bi Suan Jing and Jiu Zhang Suan Shu (including Liu Hui's annotation of the latter), and (3) the new interpretation of the Fei Niao model proposed by Shen Kuo. In addition, travel records of "intersection" observation and the technique and historical background of forward intersection were found in related historical and geographical documents. Finally, issues in the history of mathematics that are related to our topic were also discussed.