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Zhao Youqin and his calculation of \(\pi\). (English) Zbl 0885.01006

Zhao Youqin (1271-?) composed one of the two medieval Chinese texts describing procedures to determine approximate values of \(\pi\) that came down to us. The purpose of the paper is twofold. First, the author sketches a biography of this Chinese polymath who contributed to mathematics, astronomy, optics, alchemy, but also was one of the patriarchs of the Quanzhen shool of Song-Yuan Daoism. Second, A. Volkov analyses Zhao’s text devoted to \(\pi\). He shows in which respect Zhao’s procedure differs from the earlier one by Liu Hui (3rd century). Moreover, A. Volkov strives to reconstruct the way in which Zhao Youqin actually performed his computations and, in connection with this, his motivations for dealing with this topic. An appendix offers a richly annotated translation of the Chinese text.

MSC:

01A25 History of Chinese mathematics
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[1] Berëzkina, El’vira I., Dva teksta Lyu Huèya po geometrii (Two Texts on Geometry by Liu Hui), Istoriko-matematicheskie issledovaniya, 19, 231-273 (1974)
[2] Berëzkina, El’vira I., Matematika drevnego Kitaya (1980), Nauka: Nauka Moscow · Zbl 0544.01003
[3] Boltz, Judith M., A Survey of Taoist Literature. A Survey of Taoist Literature, China Research Monograph Series, 32 (1987), Univ. of California Press: Univ. of California Press Berkeley
[4] Minggui, Chen, Changchun daojiao yuanliu (1975), Guangwen shuju: Guangwen shuju Taibei
[5] Zhixu, Chen, Shangyangzi jindan dayao liexianzhi, Zheng Tong Dao Zang (1977), Xin wen fu: Xin wen fu Taibei, p. 518-522
[6] Cullen, Christopher, Chiu chang suan shu
[7] Cullen, Christopher, Chou pi suan ching
[8] Christopher, Cullen, 1995, TheZhou Bi; Christopher, Cullen, 1995, TheZhou Bi
[9] Davis, Tenney L.; Kuo-fu, Ch’ên, Shang-Yang tzû, Taoist Writer and Commentator on Alchemy, Harvard Journal of Asiatic Studies, 7, 126-129 (1942-1943)
[10] Daiwie, Fu, Problem Domain, Taxonomy, and Comparativity in Histories of Science: With a Case Study in the Comparative History of ‘Optics’, (Lin, Cheng-hung; Fu, Daiwie, Philosophy and Conceptual History of Science in Taiwan (1993), Kluwer Academic: Kluwer Academic Dordrecht), 123-147
[11] Goodrich, L. Carrington, Measurements of the Circle in Ancient China, Isis, 39, 64-65 (1948) · Zbl 0030.00101
[12] Goodrich, L. Carrington; Fang, Chaoying, Dictionary of Ming Biography, 1368-1644 (1976), Columbia Univ. Press: Columbia Univ. Press New York/London
[13] van Hée, Louis, The Ch’ou-Jen Chuan of Yüan Yüan, Isis, 8, 103-118 (1926)
[14] Akira, Hirayama, Enshuritsu-no rekishi (1980), Kyôiku tosho: Kyôiku tosho Osaka
[15] Annick, Horiuchi, 1990, Étude de Seki Takakazu (?-1708) et Takebe Katahiro (1664-1739), deux mathématiciens de l’époque d’Edo, VII, Université Paris, Paris; Annick, Horiuchi, 1990, Étude de Seki Takakazu (?-1708) et Takebe Katahiro (1664-1739), deux mathématiciens de l’époque d’Edo, VII, Université Paris, Paris
[16] Horiuchi, Annick, Les mathématiques japonaises à l’époque d’Edo (1994), Vrin: Vrin Paris · Zbl 0817.01001
[17] Jami, Catherine, Une histoire chinoise du ‘nombrePI, Archive for History of Exact Sciences, 38, 39-50 (1988) · Zbl 0698.01004
[18] Jami, Catherine, Les Méthodes rapides pour la trigonométrie et le rapport précis du cercle (1774): Tradition chinoise et apport occidental en mathématiques. Les Méthodes rapides pour la trigonométrie et le rapport précis du cercle (1774): Tradition chinoise et apport occidental en mathématiques, Mémoires de l’Institut des Hautes Études Chinoises, 32 (1990), Collège de France: Collège de France Paris · Zbl 0862.01002
[19] Tingxi, Jiang, Gu jin tushu jicheng (1964), Wen xing shudian: Wen xing shudian Taibei
[20] Qiupeng, Jin, Optics, Ancient China’s Technology and Science (1983), Foreign Language Press: Foreign Language Press Beijing, p. 166-175
[21] Jochi, Shigeru, 1988, Zu Chong-Zhi’sDa Ming Li (Da Ming Almanac)sic; Jochi, Shigeru, 1988, Zu Chong-Zhi’sDa Ming Li (Da Ming Almanac)sic
[22] Shigeru, Jochi, Zu Chongzhi deDa Ming LiDa Ming Li, Beijing shifan daxue xuebao (Ziran kexue ban), 4, 85-89 (1989) · Zbl 0714.01002
[23] Jiangxi tongzhi (1967), Huawen shuju: Huawen shuju Taibei
[24] (Baocong, Qian, Suan jing shi shu (1963), Zhonghua shuju: Zhonghua shuju Beijing), 81-258
[25] Hideki, Kawahara, (Kiyoshi, Yabuuchi, Ryû Ki chû Kyû Shô San Jutsu
[26] Lay-Yong, Lam; Tian-Se, Ang, Circle Measurements in Ancient China, Historia Mathematica, 13, 325-340 (1986) · Zbl 0632.01002
[27] Langlois, John D.; K’o-K’uan, Sun, Three Teachings Syncretism and the Thought of Ming T’ai-tsu, Harvard Journal of Asiatic Studies, 43, 97-139 (1983)
[28] Yan, Li, Zhongguo suanxue shi (1937), Shangwu: Shangwu Shanghai
[29] Yan, Li, Zhongguo shuxue dagang (1958), Kexue: Kexue Beijing
[30] Yan, Li, Zhongguo gudai shuxue shiliao (1963), Kexue jishu: Kexue jishu Shanghai
[31] Yan, Li; Shiran, Du, Chinese Mathematics: A Concise History (1987), Clarendon Press: Clarendon Press Oxford
[32] Dun, Liu, Zhao Youqin [a biographical entry], (Shiran, Du, Zhongguo gudai kexuejia zhuanji (1992), Kexue: Kexue Beijing), 690-694
[33] Xu, Liu, Jiu Tang shu (1975), Zhonghua shuju: Zhonghua shuju Beijing
[34] Zhongguo fangzhi congshu, 80 (1983)
[35] Zhongguo fangzhi congshu, 603 (1983)
[36] Yisheng, Mao, Zhongguo yuanzhoulü lüeshi (A Short History of π in China), Kexue, 3, 411-423 (1917)
[37] Martzloff, Jean-Claude, Histoire des mathématiques chinoises (1987), Masson: Masson Paris · Zbl 0653.01004
[38] Yoshio, Mikami, The Circle-Squaring of the Chinese, Bibliotheca Mathematica (III. Folge), 10, 193-200 (1910)
[39] Yoshio, Mikami, Mathematics in China and Japan (1913), Teubner: Teubner Leipzig
[40] Yoshio, Mikami, The Ch’ou-Jen Chuan of Yüan Yüan, Isis, 11, 123-126 (1928)
[41] Needham, Joseph, Mathematics and the Sciences of the Heaven and the Earth, (Needham, Joseph, Science and Civilisation in China, 3 (1959), Cambridge Univ. Press: Cambridge Univ. Press Cambridge) · Zbl 0099.24101
[42] Needham, Joseph, Chemistry and Chemical Technology, (Needham, Joseph, Science and Civilisation in China, 5 (1976), Cambridge Univ. Press: Cambridge Univ. Press Cambridge) · Zbl 0099.24101
[43] Ozawa, Yasumi, Shimotsuma, Yorikazu, 1984, A Study on the Accuracy of the Number π a paper presented at the Third International Conference on the History of Science in China, unpublished manuscript, Beijing; Ozawa, Yasumi, Shimotsuma, Yorikazu, 1984, A Study on the Accuracy of the Number π a paper presented at the Third International Conference on the History of Science in China, unpublished manuscript, Beijing
[44] Baocong, Qian, Zhongguo suanshuzhongzhi zhoulü yanjiu (A Study of π Found in Chinese Mathematical Books), Kexue, 8 (1923)
[45] Qian Baocong kexueshi lunwen xuanji (1983), Kexue: Kexue Beijing, p. 50-74
[46] Baocong, Qian, Zhonggo shuxue shi (1964), Kexue: Kexue Beijing
[47] Quzhou fuzhi. Quzhou fuzhi, Zhongguo fangzhi congshu, 602 (1983)
[48] Erwin, Reifler, 1965-1967, The Philological and Mathematical Problems of Wang Mang’s Standard Grain Measures, Symposium in Honor of Dr. Li Chi on His Seventieth Birthday, 1, 387, 402, Qinghua xuebao she, Taibei; Erwin, Reifler, 1965-1967, The Philological and Mathematical Problems of Wang Mang’s Standard Grain Measures, Symposium in Honor of Dr. Li Chi on His Seventieth Birthday, 1, 387, 402, Qinghua xuebao she, Taibei
[49] Yuan, Ruan, Chouren zhuan (1955), Shangwu: Shangwu Shanghai
[50] Schipper, Kristofer M., Concordance du Tao-Tsang (1975), École française d’Extrême-Orient: École française d’Extrême-Orient Paris
[51] Yong, Shao, Huang ji jing shi shu guan wu pian. Huang ji jing shi shu guan wu pian, Wenyuange Si ku quan shu, 803 (1986), Taiwan Shangwu yinshuguan: Taiwan Shangwu yinshuguan Taibei, p. 291-1088
[52] Volkov, Alexeı̈, Calculation of π in Ancient China: From Liu Hui to Zu Chongzhi, Historia Scientiarum, 4, 139-157 (1994) · Zbl 0824.01004
[53] Volkov, Alexeı̈, Supplementary Data on the Values of π in the History of Chinese Mathematics, Philosophy and the History of Science: A Taiwanese Journal, 3, 95-120 (1994)
[54] Alexeı̈, Volkov, 1995, Quantitative Analysis of Liu Xin’s Standard Measuring Vessels, East Asian Science: Tradition and Beyond: Papers from the Seventh International Conference on the History of Science in East Asia, Kyoto, 2-7 August 1993, Hashimoto, KeizôCatherine, JamiLowell, Skar, 387, 384, Kansai Univ. Press, Osaka; Alexeı̈, Volkov, 1995, Quantitative Analysis of Liu Xin’s Standard Measuring Vessels, East Asian Science: Tradition and Beyond: Papers from the Seventh International Conference on the History of Science in East Asia, Kyoto, 2-7 August 1993, Hashimoto, KeizôCatherine, JamiLowell, Skar, 387, 384, Kansai Univ. Press, Osaka
[55] Jianzhang, Wang, Lidai shenxian shi (1987), Xin wen feng: Xin wen feng Taibei
[56] Jinguang, Wang, Zhao Youqin ji qi guangxue yanjiu (Zhao Youqin and His Research in Optics), Kejishi wenji, 12, 93-99 (1984)
[57] Jinguang, Wang, Optics in China Based on Three Ancient Books, (Chen, Cheng-Yih, Science and Technology in Chinese Civilization (1987), World Scientific: World Scientific Singapore), 143-153 · Zbl 0608.01002
[58] Qi, Wang, Xu Wen xian tong kao (1991), Xiandai: Xiandai Beijing
[59] Qiugui, Wang; Fengmao, Li, Zhongguo minjian xinyang ziliao huibian (1989), Taiwan xuesheng shu: Taiwan xuesheng shu Taibei
[60] Shizhen, Wang, Huitu liexian quanzhuan (1971), Zhengda: Zhengda Kyôto: Chûmon, and Taibei
[61] Zheng, Wei, Sui shu (1973), Zhonghua shuju: Zhonghua shuju Beijing
[62] Wilhelm, Richard, The I Ching, or Book of Changes. The I Ching, or Book of Changes, Bollingen Series, 19 (1972), Princeton Univ. Press: Princeton Univ. Press Princeton
[63] Chunfang, Xu, Yuanzhoulü de yange (History of π), (Chunfang, Xu, Zhongsuanjia de jihexue yanjiu (1954), Zhongguo qingnian: Zhongguo qingnian Beijing), 47-57
[64] Dao, Xu, Shen xian jian (1975), Guangwen shuju: Guangwen shuju Taibei
[65] Yibao, Xu, Zhao Youqin shenghuo niandai yu jiguan (On the Dates of Life and the Birthplace of Zhao Youqin), (Di, Li, Tongxiang xiandai kexue zhi lu de tansuo (1993), The Univ. of Inner Mongolia Press: The Univ. of Inner Mongolia Press Huhehaote), 54-60
[66] Dunjie, Yan, Sui shu ‘‘Lü li zhi’ Zu Chongzhi yuanlü jishi shi (Explanation of the Note Concerning the π of Zu Chongzhi in theHistory of the Sui Dynasty, Xueyi, 15, 27-57 (1936)
[67] He, Yin, Woguo shisi shiji kexuejia Zhao Youqin de guangxue shiyan (Optical Experiments of Zhao Youqin, A Chinese Scholar of the 14th Century), Wuli tongbao (1956), p. 201-204
[68] Rong, Yong, Si ku quan shu jianming mulu
[69] Yushkevich, Adol’f P., O dostizheniyakh kitaı̈skikh uchenykh v oblasti matematiki (On the Achievements of Chinese Scholars in the Domain of Mathematics), Istoriko-matematicheskie issledovaniya, 8, 539-572 (1955) · Zbl 0066.00402
[70] Iz istorii nauki i tekhniki Kitaya (1955), Academy of Sciences: Academy of Sciences Moscow, p. 130-159
[71] Yushkevich, Adol’f P., Istoriya matematiki v srednie veka (1961), GIFML: GIFML Moscow
[72] You-Liang, Zha, Research on Tsu Ch’ung-Chih’s Approximate Method for pi, (Chen, Cheng-Yih, Science and Technology in Chinese Civilization (1987), World Scientific: World Scientific Singapore), 77-86
[73] Guangbao, Zhang, Jin Yuan quanzhendao neidan xinxinglun yanjiu (1993), Wenjin: Wenjin Taibei
[74] Xingcheng, Zhang, Huang ji jing shi guan wu wai pian yan yi. Huang ji jing shi guan wu wai pian yan yi, Wenyuange Si ku quan shu, 804 (1986), Taiwan Shangwu yinshuguan: Taiwan Shangwu yinshuguan Taibei, p. 273-309
[75] Youqin, Zhao, Chongxiu Ge Xiang Xin Shu. Chongxiu Ge Xiang Xin Shu, Wenyuange Si ku quan shu, 786 (1986), Taiwan Shangwu yinshuguan: Taiwan Shangwu yinshuguan Taibei, p. 37-197
[76] Youqin, Zhao, Ge xiang xin shu. Ge xiang xin shu, Wenyuange Si ku quan shu, 786 (1986), Taiwan Shangwu yinshuguan: Taiwan Shangwu yinshuguan Taibei, p. 221-271
[77] Youqin, Zhao, Xian Fo tong yuan lun. Xian Fo tong yuan lun, Dao shu quan ji (1990), Zhongguo shudian: Zhongguo shudian Beijing, p. 460-484
[78] (Baocong, Qian, Suan jing shi shu (1963), Zhonghua shuju: Zhonghua shuju Beijing), 1-80
[79] Zhou li zhu shu. Zhou li zhu shu, Wenyuange Si ku quan shu, 90 (1986), Taiwan Shangwu yinshuguan: Taiwan Shangwu yinshuguan Taibei, p. 1-795
[80] Zhou yi zhu shu. Zhou yi zhu shu, Wenyuange Si ku quan shu, 7 (1986), Taiwan Shangwu yinshuguan: Taiwan Shangwu yinshuguan Taibei, p. 283-584
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