Zhao Youqin and His Calculation of π

Historia Mathematica

Volumn 24, Issue 3, 1997, Pages 301-331

  Volkov, Alexeï ^a  

^a NONE

Author keywords

Zhao Youqin; Zu Chongzhi; Liu Hui; history of Chinese mathematics; calculation of approximate values of ; Daoism (Taoism); alchemy; Quan zhen; Ge xiang xin shu

Indexed keywords

EID: 0039472065     PISSN: 03150860     EISSN: None     Source Type: Journal    
DOI: 10.1006/hmat.1997.2163     Document Type: Article

References (80)

1. Berëzkina El'vira I. Dva teksta Lyu Huèya po geometrii (Two Texts on Geometry by Liu Hui). Istoriko-matematicheskie issledovaniya. 19:1974;231-273.
2. Berëzkina El'vira I. Matematika drevnego Kitaya. 1980;Nauka, Moscow.
3. Boltz Judith M. A Survey of Taoist Literature. China Research Monograph Series. 32:1987;Univ. of California Press, Berkeley.
4. Minggui Chen. Changchun daojiao yuanliu. 1975;Guangwen shuju, Taibei.
5. Zhixu Chen. Shangyangzi jindan dayao liexianzhi. Zheng Tong Dao Zang. 1977;Xin wen fu, Taibei. p. 518-522.
6. Cullen Christopher. Chiu chang suan shuJiu zhang suan shu. Early Chinese Texts. Early China Special Monograph Series. 2:1993;University of CaliforniaThe Society for the Study of Early China and The Institute of East Asian Studies, Berkeley. p. 16-23.
7. Cullen Christopher. Chou pi suan chingZhou bi suan jing. Loewe M. Early Chinese Texts. Early China Special Monograph Series. 2:1993;33-38 University of CaliforniaThe Society for the Study of Early China and The Institute of East Asian Studies, Berkeley.
8. Christopher, Cullen, 1995, TheZhou Bi, 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, 429, 434, Kansai Univ. Press, Osaka.
9. Davis Tenney L., Kuo-fu Ch'ên. Shang-Yang tzû, Taoist Writer and Commentator on Alchemy. Harvard Journal of Asiatic Studies. 7:1942-1943;126-129.
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;123-147 Kluwer Academic, Dordrecht.
11. Goodrich L. Carrington. Measurements of the Circle in Ancient China. Isis. 39:1948;64-65.
12. Goodrich L. Carrington, Fang Chaoying. Dictionary of Ming Biography, 1368-1644. 1976;Columbia Univ. Press, New York/London.
13. van Hée Louis. The Ch'ou-Jen Chuan of Yüan Yüan. Isis. 8:1926;103-118.
14. Akira Hirayama. Enshuritsu-no rekishi. 1980;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.
16. Horiuchi Annick. Les mathématiques japonaises à l'époque d'Edo. 1994;Vrin, Paris.
17. Jami Catherine. Une histoire chinoise du 'nombrePI. Archive for History of Exact Sciences. 38:1988;39-50.
18. Jami Catherine. 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, Paris.
19. Tingxi Jiang. Gu jin tushu jicheng. 1964;Wen xing shudian, Taibei.
20. Qiupeng Jin. Optics. Ancient China's Technology and Science. 1983;Foreign Language Press, Beijing. p. 166-175.
21. Jochi, Shigeru, 1988, Zu Chong-Zhi'sDa Ming Li (Da Ming Almanac)sic, a paper presented at the, 5th International Conference on the History of Science in China, San Diego, 1988.
22. Shigeru Jochi. Zu Chongzhi deDa Ming LiDa Ming Li. Beijing shifan daxue xuebao (Ziran kexue ban). 4:1989;85-89.
23. Jiangxi tongzhi. 1967;Huawen shuju, Taibei.
24. Baocong Qian. Suan jing shi shu. 1963;81-258 Zhonghua shuju, Beijing.
25. Hideki Kawahara. Kiyoshi Yabuuchi. Ryû Ki chû Kyû Shô San JutsuJiu zhang suan shu. Kagaku no meicho. 2:1980;75-264 Asahi, Tokyo.
26. Lay-Yong Lam, Tian-Se Ang. Circle Measurements in Ancient China. Historia Mathematica. 13:1986;325-340.
27. Langlois John D. Jr., K'o-K'uan Sun. Three Teachings Syncretism and the Thought of Ming T'ai-tsu. Harvard Journal of Asiatic Studies. 43:1983;97-139.
28. Yan Li. Zhongguo suanxue shi. 1937;Shangwu, Shanghai.
29. Yan Li. Zhongguo shuxue dagang. 1958;Kexue, Beijing.
30. Yan Li. Zhongguo gudai shuxue shiliao. 1963;Kexue jishu, Shanghai.
31. Yan Li, Shiran Du. Chinese Mathematics: A Concise History. 1987;Clarendon Press, Oxford.
32. Dun Liu. Zhao Youqin [a biographical entry]. Shiran Du. Zhongguo gudai kexuejia zhuanji. 1992;690-694 Kexue, Beijing.
33. Xu Liu. Jiu Tang shu. 1975;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. 3:1917;411-423.
37. Martzloff Jean-Claude. Histoire des mathématiques chinoises. 1987;Masson, Paris.
38. Yoshio Mikami. The Circle-Squaring of the Chinese. Bibliotheca Mathematica (III. Folge). 10:1910;193-200.
39. Yoshio Mikami. Mathematics in China and Japan. 1913;Teubner, Leipzig.
40. Yoshio Mikami. The Ch'ou-Jen Chuan of Yüan Yüan. Isis. 11:1928;123-126.
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.
42. Needham Joseph. Chemistry and Chemical Technology. Needham Joseph. Science and Civilisation in China. 5:1976;Cambridge Univ. Press, Cambridge.
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.
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, Beijing. p. 50-74.
46. Baocong Qian. Zhonggo shuxue shi. 1964;Kexue, Beijing.
47. 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.
49. Yuan Ruan. Chouren zhuan. 1955;Shangwu, Shanghai.
50. Schipper Kristofer M. Concordance du Tao-Tsang. 1975;École française d'Extrême-Orient, Paris.
51. Yong Shao. Huang ji jing shi shu guan wu pian. Wenyuange Si ku quan shu. 803:1986;Taiwan Shangwu yinshuguan, Taibei. p. 291-1088.
52. Volkov Alexeï. Calculation of π in Ancient China: From Liu Hui to Zu Chongzhi. Historia Scientiarum. 4:1994;139-157.
53. Volkov Alexeï. Supplementary Data on the Values of π in the History of Chinese Mathematics. Philosophy and the History of Science: A Taiwanese Journal. 3:1994;95-120.
54. Alexeï, 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, Taibei.
56. Jinguang Wang. Zhao Youqin ji qi guangxue yanjiu (Zhao Youqin and His Research in Optics). Kejishi wenji. 12:1984;93-99.
57. Jinguang Wang. Optics in China Based on Three Ancient Books. Chen Cheng-Yih. Science and Technology in Chinese Civilization. 1987;143-153 World Scientific, Singapore.
58. Qi Wang. Xu Wen xian tong kao. 1991;Xiandai, Beijing.
59. Qiugui Wang, Fengmao Li. Zhongguo minjian xinyang ziliao huibian. 1989;Taiwan xuesheng shu, Taibei.
60. Shizhen Wang. Huitu liexian quanzhuan. 1971;Zhengda, Kyôto: Chûmon, and Taibei.
61. Zheng Wei. Sui shu. 1973;Zhonghua shuju, Beijing.
62. Wilhelm Richard. The I Ching, or Book of Changes. Bollingen Series. 19:1972;Princeton Univ. Press, Princeton.
63. Chunfang Xu. Yuanzhoulü de yange (History of π). Chunfang Xu. Zhongsuanjia de jihexue yanjiu. 1954;47-57 Zhongguo qingnian, Beijing.
64. Dao Xu. Shen xian jian. 1975;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;54-60 The Univ. of Inner Mongolia Press, Huhehaote.
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. 15:1936;27-57.
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 muluSi ku quan shu. 1985;Guji, Shanghai.
69. Yushkevich Adol'f P. O dostizheniyakh kitaïskikh uchenykh v oblasti matematiki (On the Achievements of Chinese Scholars in the Domain of Mathematics). Istoriko-matematicheskie issledovaniya. 8:1955;539-572.
70. Iz istorii nauki i tekhniki Kitaya. 1955;Academy of Sciences, Moscow. p. 130-159.
71. Yushkevich Adol'f P. Istoriya matematiki v srednie veka. 1961;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;77-86 World Scientific, Singapore.
73. Guangbao Zhang. Jin Yuan quanzhendao neidan xinxinglun yanjiu. 1993;Wenjin, Taibei.
74. Xingcheng Zhang. Huang ji jing shi guan wu wai pian yan yi. Wenyuange Si ku quan shu. 804:1986;Taiwan Shangwu yinshuguan, Taibei. p. 273-309.
75. Youqin Zhao. Chongxiu Ge Xiang Xin Shu. Wenyuange Si ku quan shu. 786:1986;Taiwan Shangwu yinshuguan, Taibei. p. 37-197.
76. Youqin Zhao. Ge xiang xin shu. Wenyuange Si ku quan shu. 786:1986;Taiwan Shangwu yinshuguan, Taibei. p. 221-271.
77. Youqin Zhao. Xian Fo tong yuan lun. Dao shu quan ji. 1990;Zhongguo shudian, Beijing. p. 460-484.
78. Baocong Qian. Suan jing shi shu. 1963;1-80 Zhonghua shuju, Beijing.
79. Zhou li zhu shu. Wenyuange Si ku quan shu. 90:1986;Taiwan Shangwu yinshuguan, Taibei. p. 1-795.
80. Zhou yi zhu shu. Wenyuange Si ku quan shu. 7:1986;Taiwan Shangwu yinshuguan, Taibei. p. 283-584.