An Astronomical Problem in a Japanese Traditional Mathematical Text: The 49th Problem of the Kenki-sanpo of Takebe Katahiro

摘要

During the Edo period (Tokugawa-shogunate period) (1603-1867), there was a mathematical tradition now called "Wasan" which was primarily based on Chinese mathematics, but Japanese mathematicians also created new devices. It was quite popular, and common people could enjoy solving mathematical problems through Wasan regardless of their social status. Some astronomical problems were also treated there. In this paper, I would like to explain one problem solved by Takebe Katahiro (1664-1739), who was one of the leading disciples of the celebrated mathematician Seki Takakazu (ca. 1640-1708). The problem is to obtain the grand epoch from some fragmental data of a draft of an annual calendar from an astronomical point of view, and is the process of solving simultaneous congruence expressions from a mathematical point of view. This is not so difficult to understand astronomically, but it was extremely hard to make the necessary numerical calculations (without access to an electronic computer, of course). Here, we can see that astronomy offered interesting problems for mathematicians. Although certain areas of calendrical astronomy might have been monopolized by Government officials, others could enjoy making astronomical calculations through Wasan, which was basically open to the public.