ESHS/HSS Annual Meeting

Geometrical diagrams in traditional Chinese and Japanese mathematics

• In Event: GRAPHICS AND TEXT TWENTY YEAR LATER-2: Diagrams, Figures, Plans And Graffiti In Translation

English Abstract

The present paper is devoted to the diagrams found in Chinese mathematical treatises compiled prior to the mid-first millennium CE and in the Japanese mathematical treatises compiled in the second millennium CE. Some diagrams of the two-dimensional geometrical objects found in the extant editions of the ancient Chinese mathematical texts contained a square grid that played a particular part in mathematical demonstrations of Liu Hui 劉徽 and Zhao Shuang 趙爽 (both active in the early first millennium CE). It should be noted, however, that the original drawings of Liu Hui mentioned in his commentaries on the treatise Jiu zhang suan shu 九章算術 of the late first millennium BCE are no longer extant, and his diagrams were restored in the 18th century by Dai Zhen 戴震 (19.01.1724-01.07.1777). Several mathematical texts compiled by the later Chinese authors contained descriptions of the mathematical methods that involved manipulations with the geometrical diagrams.
Books on traditional Japanese mathematics (known as wasan 和算) of the second millennium also contained geometrical diagrams of various kinds. In my presentation I shall especially focus on the Japanese mathematical texts devoted to the methods of remote surveying that contained numerous diagrams presumably used to justify the validity of these methods. According to my evaluation, the number of the extant wasan texts related to the methods of remote surveying is quite large: there exist more than 400 texts whose titles contain the term 測 (Chinese ce, Japanese soku) referring to the remote surveying performed with the help of particular tools. To the best of my knowledge, numerous geometrical diagrams found in these texts were not properly discussed or even mentioned in the Western publications on the history of mathematics.

Author

• Alexei Volkov