Article ID: CBB000651654

Geometrical Figures and Generality in Ancient China and Beyond: Liu Hui and Zhao Shuang, Plato and Thabit ibn Qurra (2005)

unapi

Chemla, Karine Carole (Author)


Science in Context
Volume: 18
Pages: 123--166


Publication Date: 2005
Edition Details: Special Issue: Early Science
Language: English

This paper argues that there was a shift in China in the nature, and use, of geometrical figures between around the beginning of the Common Era and the third century. Moreover, I suggest that the emphasis mathematicians in ancient China placed on generality as a guiding theoretical value may account for this shift. To make this point, I first give a new interpretation of a text often discussed, which is part of the opening section of The Gnomon of the Zhou (first century B.C.E. or C.E.). This interpretation suggests that the argument presented in this text for establishing the so-called Pythagorean theorem is based upon a certain kind of drawing. Secondly, I contrast this passage with Chinese texts from the third century on the same topic, but relying on a completely different type of drawing. What commands the difference in the kinds of drawing is that the latter drawings are more general than the former, in a sense to be made explicit. This paper hence aims at making a contribution to the study of geometrical figures in ancient China. Commenting on one of the latter figures, one of the authors of the third century, Liu Hui, describes how various algorithms emerge out of the same transformation of one particular figure. His remarks provide grounds for commenting on the link between the general and the particular, in relation to figures and how algorithms rely on them, as the issue was perceived by the practitioners themselves. The particular figure in question and its transformation are exactly what we find in the Meno, though in relation to a different mathematical issue. The link of that very figure to the one that is perceived as its generalization for several algorithms, including the so-called Pythagorean theorem, is made not only in Liu Hui, but also by Thabit ibn Qurra (ninth century C.E.), in a letter where he explicitly addresses the purpose of generalizing the reasoning of the Meno. This parallel offers an appropriate basis to highlight differences in terms of conception and use of figures.

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Article Netz, Reviel; Cuomo, Serafina (2005) Early Science: A Universal History of Particulars. Science in Context (p. 1). unapi

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Authors & Contributors
Di Giacomo, Francesco
Cooper, Neil
Horky, Phillip Sidney
Zhu, Yiwen
Zhou, Chang
Unguru, Sabetai
Concepts
Mathematics
Philosophy
Geometry
East Asia, civilization and culture
Pythagoreanism
Natural philosophy
Time Periods
Ancient
Six dynasties (China, 220-589)
Neolithic period
Early modern
Modern
Medieval
Places
Greece
China
Scotland
Europe
India
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