The Influence of Indian Trigonometry on Chinese Calendar-Calculations in the Tang Dynasty

Duan Yao-Yong () and Li Wen-Lin ()
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Duan Yao-Yong: The Chinese People’s Armed Police Force Academy
Li Wen-Lin: Chinese Academy of Sciences, Academy of Mathematics and System Sciences

A chapter in Ancient Indian Leaps into Mathematics, 2009, pp 45-54 from Springer

Abstract: Summary Several historians of mathematics including Dr. J. Needham have been interested in investigating the question: How much trigonometry did the Tang astronomers know and where did they learn it? It is an interesting topic concerning cultural exchanges in history. Based on studies of trigonometry in ancient India and its transmission to China in the eighth century, this paper presents a systematic comparison of the Indian trigonometric, system with the Chinese system of “Gou–Gu.” In particular, it compares the Indian table of Rsinθ and the Chinese table of tangents in the Tang dynasty, whereby the authors point out the equivalence of the Indian trigonometric system to the Chinese system of “Gou–Gu” and try to answer Dr. J. Needham’s question with the conclusion that Chinese calendar-making and mathematics were not much influenced by Indian trigonometry due to differences in their basic concepts and systems, in spite of the fact that Indian trigonometry did appear in the Chiuchi calendar as well as in the Kaiyuan Zhanjing (the Treatise on Astrology of the Kaiyuan Era) in the form of calendrical calculation. The paper gives, in addition, a tentative analysis of the reasons why the Chinese never accepted Indian trigonometry.

Keywords: Chinese Scholar; Tang Dynasty; Actual Longitude; Ancient History; Eighth Century (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1007/978-0-8176-4695-0_3

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