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Studies in the History of Natural Sciences  2019, Vol. 38 Issue (2): 172-188    DOI:
ARTICLES     
An In-depth Study on Indian kut·t·aka and Comparison with the Chinese Da-yan Rule
LÜ Peng, JI Zhigang
School of History and Culture of Science, Shanghai Jiao Tong University, Shanghai 200240, China
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Abstract  The word Kut·t·aka means the problem of first order indefinite analysis and also the operational algorithm of this kind of problem in the works of ancient Indian mathematics. After it first appeared inĀryabhat·a's Āryabhat·īya (5th century A.D.), Kut·t·aka was an important topic for Indian mathematicians. Based on Sanskrit texts, we discuss aspects of the origin, improvement, main features and effectiveness of the Kut·t·aka algorithm. Then, comparing Kut·t·aka with the Chinese Dayan-Zongshu method, we confirm the similarity between Kut·t·aka and the Da-yan Rule on the computation of the Euclidean Algorithm, as well as in their systematic design (i.e., iterative computation) and graphically (i.e., the creeper of remainders and the square of manipulating numbers). In fact, the Dayan-Qiuyi method is a special kind of Kut·t·aka; the power of the Kut·t·aka is equivalent to the Dayan Rule. However, the two are quite different in the whole structure of the algorithm and in historical development. Moreover, the Kut·t·aka method seems to be more general, simpler and easier because of a series of rules of reduction and continuity.

Key words： Kut·t·aka      Āryabhat·a      history of Indian mathematics      Dayan-Qiuyi method      Da-yan Rule (Dayan-Zongshu-shu)     
Received: 07 August 2017      Published: 18 June 2022
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LÜ Peng, JI Zhigang. An In-depth Study on Indian kut·t·aka and Comparison with the Chinese Da-yan Rule. Studies in the History of Natural Sciences, 2019, 38(2): 172-188.

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http://www.shns.ac.cn/     OR     http://www.shns.ac.cn/Y2019/V38/I2/172

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