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.
