The Japanese Mathematician Shigekiyo Muramatsu

Yesterday, Arjen Dijksman, a Twitter friend of mine, told me on twitter that the Twitter user by the name of OnThisDayInMath was looking for pictures of Matsumura's tomb, Sengakuji, and the inscription on the path, in relation to a blog article (Ref. 1). This article quotes the following description from a March 1908 article in the American Mathematical Monthly:

[O]ne of [the 47 ronin], Shigekiyo Matsumura, was the greatest Asiatic mathematician of his age, who in his work Sanso, published in 1663, calculated the length of one side of a regular inscribed polygon of 32768 or 215 sides, obtaining 0.000095873798655313483 and thence for the value of pi 3.141592648, which is accurate to seven places of decimalsone of them, Shigekiyo Matsumura, was the greatest Asiatic mathematician of his age, who in his work Sanso, published in 1663, calculated the length of one side of a regular inscribed polygon of 32768 or 215 sides, obtaining 0.000095873798655313483 and thence for the value of pi 3.141592648, which is accurate to seven places of decimals ...

I made the search of "Shigekiyo Matsumura" and "Sanso" on the Internet to find that the correct name of the author of Sanso was "Shigekiyo Muramatsu" and that he himself was not the member of the forty-seven ronin (赤穂四十七士). The most useful source of my finding was Ref. 2, my translation from which is given below (the original Japanese text is given in Appendix):

Shigekiyo Muramatsu (村松 茂清, 1608–1695) published Sanso (算俎) in 1663. Muramatsu served Asano (浅野) family and possibly had a math institute in Edo [present Tokyo]. Muramatsu had only a daughter, and took Hidenao (秀直) into his family as a son-in-law [the daughter's husband]. Hidenao and his son Takanao (高直) joined the forty-seven ronin to cause the Akō incident. In Sanso, Muramatsu arranged idai [problems published in earlier Japanese mathematics books written without answers] by classifying them into different levels with consideration for ease of learning. In this book, he also showed the calculation of pi from the regular inscribed polygon of 32768 sides to correctly obtain the value 3.1415926. Thus, this book was the first in the mathematical calculation of pi in Japan. Sanso was republished in 1684 by the title of Sanposanso (算法算俎). This item [possessed by Kyoto University Library and presented in the exhibition] is the copy of this republication, but it is not clear if this is the one published in 1684. Inside the back cover, it is written that this was bought in September 8, 1857, in Asakusa-kuramae.

We can see the names of all the forty-seven ronin in a list of a Wikipedia page (Ref. 3). The list shows Hidenao and Takanao with their middle names included as 村松 喜兵衛 秀直 and 村松 三太夫 高直, but not Shigekiyo. It is natural because the Akō incident was in 1703 (Refs. 3, 4), and Shigekiyo had died in 1695 as written in Ref. 2. Thus, I am not sure if Shigekiyo's tomb is in Sengakuji Temple together with those of the forty-seven ronin.

References

1. "Pi and the 47 Ronin." Pat's Blog (September 5, 2009).
2. The Catalog of the Exhibition "Wasan no Jidai (和算の時代, The Age of Japanese Mathematics),"edited by Kenji Ueno, Chapter 3, p 28, item 66 (Kyoto University Library, 2003) (In Japanese).
3. "赤穂浪士 (Akō-rōshi)," Wikipedia, The Free Encyclopedia, Japanese edition (March 19, 2011, 10:23).
4. "Forty-seven Ronin," Wikipedia, The Free Encyclopedia (23 April 2011, 05:32).

Appendix. The Original of Ref. 2

　村松茂清（むらまつ　しげきよ、1608－1695）は寛文３年（1663）に算俎を出版しました。村松は浅野家に仕えていましたが、江戸に数学塾を持っていたようです。村松には娘しかなく、婿養子秀直を迎えましたが、秀直と秀直の子高直は赤穂四十七士の討ち入りに参加しました。村松は「算俎」のなかで、遺題の問題を内容別にレベル分けして配列し、学習しやすいように配慮しました。「算俎」では円に内接する正32768角形の周の長さを計算して円周率を3.1415926まで正しく計算しました。円周率を数学的に計算した我が国初の書物です。「算俎」は天和４年（1684、同年貞享に改元）に「算法算俎」と題して再版されました。本書はこの再版本ですが、天和４年に出版されたものかどうかは不明です。裏表紙の裏に「安政四丁巳九月八日浅草蔵前求之」と記されています。

Notes added later

• The revised version of Ref. 1 with an addendum appeared: "More on Pi and the 47 Ronin," Pat's Blog (May 3, 2011).
• According to the Japanese Wikipedia page on Hidenao Muramatsu, Shigekiyo Matsumura had the middle name Kyūtaifu (九太夫) (the "middle name" was used as the daily nickname in those days of Japan), and he had a son. However, the son disappeared from home and was lost, so that Shigekiyo took Hidenao as a son-in-law.