Abstract
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.
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Notes
- 1.
This was the Tokugawa (徳川)-shogunate period, during which Edo (present-day Tokyo) was the headquarters of the Shōgun (which literally means “general,” but in reality is something like the king, although the nominal emperor existed in Kyoto).
- 2.
For the history of astronomy in China in general, Chen (1983) or Chen (2003) may be consulted. The former reference provides an English language introduction to the calendrical systems of China (although the Xuanming-li is not mentioned there), while the second Chen reference, in Chinese language, is probably the most comprehensive history of Chinese astronomy in a single volume that is currently available. There is no comparable work written in English, as Needham’s monumental work (1959) does not provide enough detailed information on Chinese calendars. There is also a collection of detailed monographs on the history of Chinese astronomy in Chinese by Bo (2008–2009). For earlier developments in Chinese astronomy, in English language, see Ôhashi (2007; 2008). For the history of astronomy in Korea the English language book by Jeon (1974) may be consulted, but there are many other works written in Korean. For the history of astronomy and mathematics in Japan in general, the English language books by Nakayama (1969) and Smith et al. (1914) may respectively be consulted, but there are many other works in Japanese. An English translation of the Jinkōki of Yoshida Mitsuyoshi has been published by the Wasan Institute (2000), and some of the works of Takebe Katahiro, including a rough translation of his Kenki-sanpō, have been published in English by Takenouchi and Morimoto (2004). For some aspects of the calendrical system of Shibukawa Harumi see Ôhashi (2009).
- 3.
The “grand epoch” is defined as some specified time in the remote past, and varied from one calender system to another. The grand epoch in reality was a kind of artificial epoch that was used for the sake of convenience rather than a time when specific astronomical events actually took place. In the case of the Xuanming-li calendar, the date of the grand epoch was 7,069,317 BC.
- 4.
The Kenki-sanpō dai-shijūku kaijutsu is included in a manuscript Sekisan-kōden (関算後伝) volume 69, and is preserved in the Miyagi Prefectural Library (宮城県図書館; accession number: KD090, se5, 474–245). A facsimile of this work is included in Higashi-Ajia Sūgakushi Kenkyūkai (2010).
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Acknowledgements
I am grateful to Mr Sato Ken’ichi (Director, Wasan Institute) who provided me with a photocopy of the Kenkisanpō and to Mr Yamaji Katsunori (former editor, Tokyo-shoseki) who helped with photocopying.
I am also grateful to Mr Fujii Yasuo and Mr Yokotsuka Hiroyuki who gave me valuable information including their respective unpublished drafts.
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Ôhashi, Y. (2011). An Astronomical Problem in a Japanese Traditional Mathematical Text: The 49th Problem of the Kenki-sanpo of Takebe Katahiro. In: Orchiston, W., Nakamura, T., Strom, R. (eds) Highlighting the History of Astronomy in the Asia-Pacific Region. Astrophysics and Space Science Proceedings. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8161-5_9
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