| 等差级数与插值法 |
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| 引用本文： | 刘钝.等差级数与插值法[J].自然科学史研究,1995,14(4):331-336. |
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| 作者姓名： | 刘钝 |
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| 作者单位： | 中国科学院自然科学史研究所 |
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| 摘 要： | 《周髀算经》中求“衡径”和“晷长”的方法可以视为一次插值法的应用，《大衍历》中“先定日数，径求积度及分”的方法实与刘徽提出的等差级数求和公式一致。一般来说，一个（ｋ—１）阶等差级数的求和公式等价于一个ｋ阶等间距插值公式。在中国古代数学中，等差级数和插值法是两个相互关联的题材，宋元数学家在充分认识高阶等差级数的基础上方有可能得到一般的等间距插值公式。
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| 关 键 词： | 等差级数，插值法 |
ARITHMETICAL SERIES AND INTERPOLATION |
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| Liu Dun.ARITHMETICAL SERIES AND INTERPOLATION[J].Studies In The History of Natural Sciences,1995,14(4):331-336. |
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| Authors: | Liu Dun |
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| Abstract: | The method for finding"heng-diameter"and"gui-length"in the Zhou Bi Suan Jing(Arithmetical Classic of the Zhou Gnomon)can be regarded as an application of linear interpolation, while that for finding sun's displacement in the Dayan Calendar is similar to the sum formula of arithmetical series proposed by Liu Hui.Generally,the sum formula of a k-1 degree arithmetical series is equal to that of a k degree interpolation with equidifferences.In ancient Chinese mathematics,arithmetical series and interpolation are two interrelated topics.It was only based on sufficient knowledge of higher degree arithmetical series that the mathmaticians of the Song and Yuan Dynasties were able to reach the general result of interpolation with equidifferences. |
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| Keywords: | arithmetical series interpolation |
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