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한국과학사학회지, 제45권 제3호 (2023), 451-479
중수대명력의 영축 보간법 고찰
by 김동빈, 전준혁
| 첨부파일 '1' |
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| 초록 | We examined the mathematical method of creating the Yeongchuk-Ipseong 盈縮-立成 (Yeongchuk means “profit and loss” in the movement of the Sun, and Ipseong refers to the table) of the Chongxiu-Daming-li 重修大明曆 using the divided difference principle. Accordingly, we identified the mathematical meaning of the fundamental quantities used in the Yeongchuk interpolation. The method of calculating the daily Yeongchuk-Jonyuk 盈縮-眺朒 (Jonyuk is a temporal quantity corresponding to solar inequality, which is converted via the angular velocity of the Moon) in the Chongxiu-Daming-li is mathematically the same procedure as creating a divided difference table for Yeongchuk-Jonyuk. The interpolation method for Yeongchuk-Jonyuk in the Chongxiu-Daming-li is mathematically identical to modern quadratic interpolation. The limit of the interpolation error is less than ±0.001°, and the difference is similar to the results obtained by the modern second-order polynomial interpolation method. The accuracy of the Yeongchuk interpolation had already reached a high level in the Chongxiu-Daming-li. This suggests that the Shoushi-li 授時曆 did not address the fundamental problem of the Chongxiu-Daming-li in calculating the position of the Sun. The conventional assessment that adopting the third-order interpolation in the Shoushi-li would have improved the accuracy of the solar position should be reconsidered. |
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| 주요어 | Chinese calendar, Chongxiu-Daming-li, solar anomaly, polynomial interpolation, divided difference method, Chinese numerical method |
중수대명력의 영축 보간법 고찰
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