中国の数学
出典: フリー百科事典『ウィキペディア（Wikipedia）』 (2024/01/11 18:50 UTC 版)
中国の数学（ちゅうごくのすうがく、英:Chinese mathematics）とは、紀元前11世紀までに現在の中国で独立して興り、独自に発展した数学のこと[1]。具体的な独自発展には、非常に大きい数および負の数を含む数の設定、十進法、十進法体系の位取り記数法、二進法、代数、幾何学、三角法などがある。
注釈
出典
- ^ Chinese overview
- ^ a b c Chemla, Karine. “East Asian Mathematics”. Britannica Online Encyclopedia. 2019年5月11日閲覧。
- ^ a b c d e f g h Needham, Joseph (1959). Science and Civilization in China. England: Cambridge University Press. pp. 1-886. ISBN 0 521 05801 5
- ^ a b c d e f Needham, Joseph (1955). “Horner's Method in Chinese Mathematics”. T'oung Pao, Second Series 43 (5): 345-401. JSTOR 4527405.
- ^ Frank J. Swetz and T. I. Kao: Was Pythagoras Chinese?
- ^ 日本大百科全書(ニッポニカ)『墨子』 - コトバンク
- ^ Needham, Volume 3, 91.
- ^ a b c Needham, Volume 3, 92.
- ^ Needham, Volume 3, 92-93.
- ^ Needham, Volume 3, 93.
- ^ Needham, Volume 3, 93-94.
- ^ Needham, Volume 3, 94.
- ^ Jane Qiu (7 January 2014). “Ancient times table hidden in Chinese bamboo strips”. Nature. doi:10.1038/nature.2014.14482 2016年9月15日閲覧。.
- ^ Ifrah, Georges (2001). The Universal History of Computing: From the Abacus to the Quantum Computer. New York, NY: John Wiley & Sons, Inc.. ISBN 978-0471396710
- ^ a b c d e f g h i j k l Hart, Roger. The Chinese Roots of Linear Alegbra. John's Hopkins University. pp. 11-85. ISBN 978 0801897559
- ^ a b c d e Lennart, Bergren (1997). Pi: A Source Book. New York. ISBN 978-1-4757-2738-8
- ^ a b c d Lay Yong, Lam (June 1994). “Nine Chapters on the Mathematical Art: An Overview”. Archive for History of Exact Sciences 47 (1): 1-51. doi:10.1007/BF01881700. JSTOR 41133972.
- ^ a b c Siu, Man-Keung (1993). “Proof and Pedagogy in Ancient China”. Educational Studies in Mathematics 24 (4): 345-357. doi:10.1007/BF01273370. JSTOR 3482649.
- ^ a b c d Dauben, Joseph W. (2008). “算数書 Suan Shu Shu A Book on Numbers and Computations: English Translation with Commentary”. Archive for History of Exact Sciences 62 (2): 91-178. doi:10.1007/s00407-007-0124-1. JSTOR 41134274.
- ^ 城地茂「『算数書』日本語訳」、大阪教育大学『和算研究所紀要』4(2001年)、19-46頁。 39頁の「分銭」「米出銭」「方田」が過不足算を使って解く問題となっている（同資料では、原文に合わせて「盈不足」という昔の用語を使っている）。
- ^ 大川俊隆「『九章算術』訳注稿（1）」、大阪産業大学『大阪産業大学論集 人文・社会科学編』2、2007年10月31日（原稿受理）。11頁
- ^ a b c d e Dauben, Joseph (2013). “九章算術 "Jiu zhang suan shu" (Nine Chapters on the Art of Mathematics)An Appraisal of the Text, its Editions, and Translations”. Sudhoffs Archiv 97 (2): 199?235. JSTOR 43694474. PMID 24707775.
- ^ Straffin, Philip D. (1998). “Liu Hui and the First Golden Age of Chinese Mathematics”. Mathematics Magazine 71 (3): 163-181. doi:10.2307/2691200. JSTOR 2691200.
- ^ a b Yong, Lam Lay (1970). “The Geometrical Basis of the Ancient Chinese Square-Root Method”. Isis 61 (1): 92-102. doi:10.1086/350581. JSTOR 229151.
- ^ 馬場理惠子「『九章算術』訳注・稿（21）」、大阪産業大学『大阪産業大学論集 人文・社会科学編』25、2015年6月30日原稿受理。22-24頁。
- ^ Frank J. Swetz: The Sea Island Mathematical Manual, Surveying and Mathematics in Ancient China 4.2 Chinese Surveying Accomplishments, A Comparative Retrospection p63 The Pennsylvania State University Press, 1992 ISBN 0-271-00799-0
- ^ 三上義夫, The Development of Mathematics in China and Japan, chap 7, p. 50, reprint of 1913 edition Chelsea, NY, Library of Congress catalog 61-13497.英文書籍で未邦訳。isbn 0828401497
- ^ Lam Lay Yong (1996). “The Development of Hindu Arabic and Traditional Chinese Arithmetic”. Chinese Science 13. オリジナルの2012-03-21時点におけるアーカイブ。 2015年12月31日閲覧。.
- ^ Alexander Karp; Gert Schubring (25 January 2014). Handbook on the History of Mathematics Education. Springer Science & Business Media. pp. 59-. ISBN 978-1-4614-9155-2
- ^ Yoshio Mikami, Mathematics in China and Japan,p53
- ^ Hugh Chisholm, ed (1911). The encyclopædia britannica: a dictionary of arts, sciences, literature and general information, Volume 26 (11 ed.). At the University press. p. 926 2011年7月1日閲覧。The Encyclopædia Britannica: A Dictionary of Arts, Sciences, Literature and General Information, Hugh Chisholm
- ^ Translated by William Woodville Rockhill, Ernst Leumann, Bunyiu Nanjio (1907). The Life of the Buddha and the early history of his order: derived from Tibetan works in the Bkah-hgyur and Bstan-hgyur followed by notices on the early history of Tibet and Khoten. K. Paul, Trench, Tr?bner. p. 211 2011年7月1日閲覧。
- ^ a b c d e Needham, Volume 3, 109.
- ^ Needham, Volume 3, 108-109.
- ^ Martzloff (1987), p. 142.
- ^ Needham, Volume 3, 43.
- ^ Needham, Volume 3, 62‐63.
- ^ Yoshio Mikami, The development of Mathematics in China and Japan, p77 Leipzig, 1912
- ^ Ulrich Librecht,Chinese Mathematics in the Thirteenth Century p. 211 Dover 1973
- ^ Needham, Volume 3, 134-137.
- ^ Needham, Volume 3, 46.
- ^ a b (Boyer 1991, "China and India" p. 204)
- ^ (Boyer 1991, "China and India" p. 203)
- ^ (Boyer 1991, "China and India" p. 205)
- ^ (Boyer 1991, "China and India" pp. 204-205) "The same "Horner" device was used by Yang Hui, about whose life almost nothing is known and who work has survived only in part. Among his contributions that are extant are the earliest Chinese magic squares of order greater than three, including two each of orders four through eight and one each of orders nine and ten."
- ^ Katz, 308.
- ^ Restivo, 32.
- ^ Gauchet, 151.
- ^ Needham, Volume 3, 110.
- ^ Martzloff (1987), p. 4.
- ^ He, Ji-Huan (May 2004). “Some interpolation formulas in Chinese ancient mathematics”. Applied Mathematics and Computation 152 (2): 367-371. doi:10.1016/s0096-3003(03)00559-9. ISSN 0096-3003.
- ^ “East Asian Journal on Applied Mathematics”. East Asian Journal on Applied Mathematics. doi:10.4208/eajam.
- ^ Martzloff (1987), p. 21.
- ^ Brucker, Joseph (1912). "Matteo Ricci". The Catholic Encyclopedia. New York: Robert Appleton Company. OCLC 174525342. Retrieved 17 August 2017.
- ^ Martzloff (1987), p. 29.
- ^ Martzloff (1987), pp. 25–8.
- ^ Jami, Catherine; Qi, Han (2003-01-01). “The Reconstruction of Imperial Mathematics in China During the Kangxi Reign (1662-1722)”. Early Science and Medicine 8 (2): 88-110. doi:10.1163/157338203X00026. ISSN 1573-3823.
- ^ Jami, Catherine (2011-12-01), A mathematical scholar in Jiangnan: The first half-life of Mei Wending, “The Emperor's New Mathematics Western Learning and Imperial Authority During the Kangxi Reign (1662-1722)”, The Emperor's New MathematicsWestern Learning and Imperial Authority During the Kangxi Reign (1662-1722) (Oxford University Press): pp. 82-101, doi:10.1093/acprof:oso/9780199601400.003.0005, ISBN 9780199601400 2018年7月28日閲覧。
- ^ 1946-, Elman, Benjamin A. (2005). On their own terms : science in China, 1550-1900. Cambridge, Mass.: Harvard University Press. ISBN 9780674036475. OCLC 443109938
- ^ Martzloff (1987), p. 28.
- ^ Minghui, Hu (2017-02-14). China's transition to modernity : the new classical vision of Dai Zhen. Seattle. ISBN 978-0295741802. OCLC 963736201
- ^ Jean-Claude Martzloff, A History of Chinese Mathematics, Springer 1997 ISBN 3-540-33782-2
- ^ Catherine, Jami (2012). The emperor's new mathematics : Western learning and imperial authority during the Kangxi Reign (1662-1722). Oxford: Oxford University Press. ISBN 9780191729218. OCLC 774104121
- ^ Carlyle, Edward Irving (1900). "Wylie, Alexander". In Lee, Sidney. Dictionary of National Biography. 63. London: Smith, Elder & Co.
- ^ "Li Shanlan's Summation Formulae". A History of Chinese Mathematics: 341?351. doi:10.1007/978-3-540-33783-6_18.
- ^ Martzloff (1987), pp. 34–9.
- ^ “Chern biography”. www-history.mcs.st-and.ac.uk. 2017年1月16日閲覧。
- ^ “12.06.2004 - Renowned mathematician Shiing-Shen Chern, who revitalized the study of geometry, has died at 93 in Tianjin, China”. www.berkeley.edu. 2017年1月16日閲覧。
- ^ J. R., Chen (1973). On the representation of a larger even integer as the sum of a prime and the product of at most two primes. Sci. Sinica
- ^ “Team Results: China at International Mathematical Olympiad”. 2019年5月11日閲覧。
- ^ a b Christopher Cullen, "Numbers, numeracy and the cosmos" in Loewe-Nylan, China's Early Empires, 2010:337-8.
[続きの解説]
「中国の数学」の続きの解説一覧
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