Calculation of the shangyuan jinian elapsed-year-since--grand-epoch of the kaixi calendar

Details Calculation of the shangyuan jinian elapsed-year-since--grand-epoch of the kaixi calendar Calculation of the shangyuan jinian elapsed-year-since--grand-epoch of the kaixi calendar

Jan 2007

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007acasn..48...93w&link_type=abstract

Acta Astronomica Sinica, vol. 48, no. 1, p.93-112

Astronomy and Astrophysics

Astronomy

History Of Astronomy, The Kaixi Calendar, Shangyuan Jinian

Scientific paper

Gauss C.F. (1777-1855) pointed out in his Disquisitiones Arithmeticae (1801) that linear congruences came from the problems of calendars: ``This usage arose in the problem of chronology when we seek to determine what Julian year it is whose indiction, golden number, and solar cycle are given.'' The Problem of Zhili Yanji (Design for a Calendar by Means of the Sexagenary Cycle) in Qin Jiushao's Shushu Jiuzhang ( Mathematical Treatise in Nine Sections ) (A.D. 1247) recorded the design development of the Kaixi Calendar (1207-1251) which was the unique existent material recorded during this period of more than 1000 years when the algorithm of Shangyuan Jinian Elapsed-Year-since--Grand-Epoch used by ancient and medieval Chinese calendarists until A.D. 1280. It is devoted to restituting the full calculation of this data by analysising original thought on concept about linear congruences for the conditions of the Grand-Epoch, the cycle consonant principle, the concept of the Qiyuan Solar-period, the reason for the Ruyuansui Entry-of-Solar-period, the Dayan method and the counting process for the Yuansu Number-of-Solar-period.

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