Abstract
Mathematical writings in China relied entirely on the algorithmic mode to express sequences of operations, to justify the correctness of these, and to bring mathematical objects in relation one to another. In this paper, I shall use one example to show how the structural elements in an algorithm convey a mathematical meaning and can be interpreted in the light of the ancient Chinese geometrical tradition. The example stems from an 11th century text by Shen Gua 沈括 and calculates the number of kegs of wine piled up in the form of a truncated pyramid with a rectangular base.
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References
Bréard, A.: Shen Gua’s Cuts. Taiwanese Journal for Philosophy and History of Science 10, 141–162 (1998)
Bréard, A.: Re-Kreation eines mathematischen Konzeptes im chinesischen Diskurs: Reihen vom 1. bis zum 19. Jahrhundert. Steiner, Stuttgart (1999)
Chemla, K., Guo, S.: Les neuf chapitres sur les procédures mathématiques. Dunod, Paris (2004)
Shen, G., Hu, D. (eds.): Mengxi bitan jiaozheng (in Chinese) (Critical Edition of Brush Talks from the Dream Pool), 2 vols. Shanghai guji chubanshe, Shanghai (1987)
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Bréard, A. (2008). A Summation Algorithm from 11th Century China. In: Beckmann, A., Dimitracopoulos, C., Löwe, B. (eds) Logic and Theory of Algorithms. CiE 2008. Lecture Notes in Computer Science, vol 5028. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69407-6_8
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DOI: https://doi.org/10.1007/978-3-540-69407-6_8
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