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

  • Duan Yao-Yong
  • Li Wen-Lin


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.


Chinese Scholar Tang Dynasty Actual Longitude Ancient History Eighth Century 
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  1. 1.
    Siddha, Gautama: Kaiyuan Zhanjing (the Treatise on Astrology of the Kaiyuan Era) (Jing Volume 104). The Chinese Bookstore Press, Beijing (1989).Google Scholar
  2. 2s.
    Souneiqing: Studies on the Chiuchi Calendar, Translation Series in the History of Science. Liaoning People’s Press, Shenyang (1985).Google Scholar

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© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.The Chinese People’s Armed Police Force AcademyLangfangChina
  2. 2.Academy of Mathematics and System SciencesChinese Academy of SciencesBeijingChina

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