【摘要】 高次招差术是元代数学家朱世杰的重要成果,《四元玉鉴》中的“如象招数”门共有5问,均是招差问题,实际上是属于高阶等差级数求和,其求和是通过招差公式(即内插法公式)进行的.经研究验算,该5问都可以用同一公式计算求得,朱世杰在这里应用了四次及五次等间距内插公式,并且对此类问题有了一个比较系统和普遍的解法.更多还原

【Abstract】 Zhu Shijie is one of the famous mathematicians in Yuan Dynasty and one of his major contributions to mathematics is the high degree "Zhaocha" method,a numerical method of finite difference.In his book Siyuan Yujian,the section of "Ruxing Zhaoshu" discussed five problems belonging to the "Zhaocha" problems.Actually,the study of these problems is to find the sums of arithmetic series of higher order and Zhu Shijie obtained the results by using "Zhaocha" formulas which indeed are the interpolation formulas.It is proved that these five problems can be solved by a identical formula,while Zhu Shijie used the interpolation formulas of four and five degrees with equally-spaced steps.It is shown that Zhu Shijie′s study established a general method for these problems systematically.更多还原