Investigating Chinese mathematical techniques to calculate sunrise and sunset times in Datongli

doi:10.1002/asna.201813480

CORC > 自然科学史研究所 > 中国科学院自然科学史研究所 > 中国古代科技史研究室

	Investigating Chinese mathematical techniques to calculate sunrise and sunset times in Datongli
	Choi, G-E.3,4; Lee, K-W.2; Mihn, B-H.3,4; Li, L.6; Ryu, Y-H.1; Ahn, Y. S.5
刊名	ASTRONOMISCHE NACHRICHTEN
	2018-07-01
卷号	339 期号:6 页码:520-532
关键词	history and philosophy of astronomy: method mathematical method: ephemerides
ISSN号	0004-6337
DOI	10.1002/asna.201813480
通讯作者	Lee, K-W.(leekw@cu.ac.kr)
英文摘要	We investigate the calculation method of sunrise and sunset times in the Datongli (Great Concordance Calendar) of the Ming dynasty focusing on Chinese mathematical techniques. Referring to the Mingshi (History of the Ming Dynasty), we found that latitude and obliquity were determined from observations of the transit altitude of the Sun on the winter and summer solstices using the Guibiao (Gnomon) and the Jianyi (Simplified Armillary Sphere) as astronomical instruments. According to the Mingshi, 12 values for the equation of center of the Sun were also determined from observations. However, these values may have been rectified, at least to utilize a cubic equation for interpolating the equation of center. With regard to Chinese mathematical techniques, we found that the Zhaocha (solving the coefficients of a cubic equation), Hushigeyuan (finding approximate solutions of a quartic equation), and Chongcha (proportional property of similar right-angled triangles) were employed to calculate the sunrise and sunset times together with the Gougu (i.e., the Pythagorean theorem) and Kaifang (i.e., square root extraction) techniques. We reproduce the sunrise and sunset times by the Datongli, and verify the numerical values of the tables in the Mingshi associated with the calculations of these times. We found that the values recorded in the Mingshi agree satisfactorily with those reproduced in this study, except for several cases considered typographical errors. We think that this study will help understand the Datongli, particularly the Chinese mathematical techniques used in it.
资助项目	Korea Government (MSIP)[2016R1A2B4010887]
WOS关键词	13TH-CENTURY
WOS研究方向	Astronomy & Astrophysics
语种	英语
出版者	WILEY-V C H VERLAG GMBH
WOS记录号	WOS:000446655100010
资助机构	Korea Government (MSIP)
内容类型	期刊论文
源URL	[http://ir.ihns.ac.cn/handle/311051/7453]
专题	中国古代科技史研究室
作者单位	1.KoreaAstron&SpaceSciInst,OptAstronDiv,Daejeon,SouthKorea; 2.DaeguCatholicUniv,InstLiberalEduc,Gyongsan,SouthKorea; 3.KoreaAstron&SpaceSciInst,CtrHistAstron,Daejeon,SouthKorea; 4.KoreaUnivSci&Technol,DeptAstron&SpaceSci,Daejeon,SouthKorea; 5.KoreaAstron&SpaceSciInst,SpaceSciDiv,Daejeon,SouthKorea 6.ChineseAcadSci,InstHistNatSci,Beijing,PeoplesRChina;
推荐引用方式 GB/T 7714	Choi, G-E.,Lee, K-W.,Mihn, B-H.,et al. Investigating Chinese mathematical techniques to calculate sunrise and sunset times in Datongli[J]. ASTRONOMISCHE NACHRICHTEN,2018,339(6):520-532.
APA	Choi, G-E.,Lee, K-W.,Mihn, B-H.,Li, L.,Ryu, Y-H.,&Ahn, Y. S..(2018).Investigating Chinese mathematical techniques to calculate sunrise and sunset times in Datongli.ASTRONOMISCHE NACHRICHTEN,339(6),520-532.
MLA	Choi, G-E.,et al."Investigating Chinese mathematical techniques to calculate sunrise and sunset times in Datongli".ASTRONOMISCHE NACHRICHTEN 339.6(2018):520-532.