朱世杰招差术探原

招差术或称内插公式是朱世杰《四元玉鉴》的重要成果，也是中国传统数学代表性成果之一，关于该术的立术之原尚有不同意见，作者认为，其立术当与中国传统数学的分割求积法及贾宪三角形之应用有关。据此，作者给出朱世杰内插公式一种推导方法。

A FURTHER INVESTIGATION ON ZHU SHIJIE'SINTERPOLATION FORMULA

One of the major contributions of Zhu Shijie in mathematics is in the numericalmethod of finite differences and interpolation. In this paper, the authors trace the derivationof Zhu's interpolation formula published in 1303 in his book Si-Yuan Yu-Jian (Reflections inMathematics up to Four Variables). It is demonstrated that the formula can be derived withinthe framework of series summation by the algorithm of dissecting figures and of recurrence relations in the Jia Xian triangle (known to the West as the Pascal triangle).