Abstract:
The mathematical methods used to calculate the distances from observers to prominent remote elements of landscapes (e.g., mountains, towers, temples) appeared in the earliest extant Chinese mathematical treatises Zhou bi suan jing 周髀算經 ("Computational Treatise on the Gnomon of the Zhou [dynasty]"), Jiu zhang suan shu 九章算術 ("Computational procedures of nine categories," also known as "Mathematics in Nine Books" or "Mathematics in Nine Chapters", etc), and Hai dao suan jing 海島算經 ("Treatise on Computations [beginning with the problem] on a Maritime Island") compiled in the late first millennium BCE and the early first millennium CE. Later the methods of this kind appeared in several Chinese mathematical texts of the mid- and late first millennium CE and in the Chinese and Japanese mathematical texts written in the first half of the second millennium CE. Historians of mathematics suggested various reconstructions of these methods: one group of researchers argued that the ancient mathematicians used methods of the so-called "geometric algebra", while the others believed that these methods were based on the concept of similarity of geometrical figures. Moreover, the numerous Japanese mathematical texts that contain discussions of methods of this kind, unfortunately, were not studied by historians of mathematics well enough.
In his presentation the author will briefly introduce the Chinese and Japanese mathematical texts devoted to the methods of remote surveying, and provide a brief analysis of the reconstructions of these methods published by modern historians of mathematics.
Keywords: mathematical methods of geodetic measurements; history of mathematics in China; history of traditional Japanese mathematics (wasan 和算); Chinese mathematical treatises "Zhou bi suan jing 周髀算經", "Jiu zhang suan shu 九章算術", and "Hai dao suan jing 海島算經".
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