和算家的累约术

Indefinite Problem in Wasan

以和算家建部贤弘和中根元珪的累约术为例,通过探讨和算家的问题来源,复原其算法的构造思想,及其处理这些问题时与中算家的不同方法和态度,说明中日两国数学家在数学创造方面的一些异同之处.和算作为继承并发展中国古代数学的一个标本,对于深刻理解机械化程序算法体系的数学传统,颇有益处.

Japanese mathematics, namely Wasan, was well-developed before the Meiji period. Takebe Katahiro （1664-1739）and Nakane Genkei （1662-1733） , among a great number of mathematicians in Wasan, maybe the most famous ones. Taking Takebe and Nakane＇s indefinite problem as examples, the similarities and differences are made between Wasan and Chinese mathematics. According to investigating the sources and attitudes to these problems which both Japanese and Chinese mathematicians dealt with, the paper tries to show how and why Japanese mathematicians accepted Chinese tradition and beyond. As a typical sample of the succession of Chinese tradition, Wasan will help people to understand the real meaning of Chinese tradition deeper.