Japanese mathematics

Japanese mathematics (和算, wasan) denotes a distinct kind of mathematics which was developed in Japan during the Edo period (1603–1867). The term wasan, from wa ("Japanese") and san ("calculation"), was coined in the 1870s^[1] and employed to distinguish native Japanese mathematical theory from Western mathematics (洋算 yōsan).^[2]

In the history of mathematics, the development of wasan falls outside the Western realm. At the beginning of the Meiji period (1868–1912), Japan and its people opened themselves to the West. Japanese scholars adopted Western mathematical technique, and this led to a decline of interest in the ideas used in wasan.

History

Pre-Edo period (552-1600)

Records of mathematics in the early periods of Japanese history are nearly nonexistent. Though it was at this time that a large influx of knowledge from China reached Japan, including that of reading and writing, little sources exist of usage of mathematics within Japan. However, it is suggested that this period saw the use of an exponential numbering system following the law of $a^{m}*a^{n}=a^{m+n}$ .^[3]

Edo period

The Japanese mathematical schema evolved during a period when Japan's people were isolated from European influences, but instead borrowed from ancient mathematical texts written in China, including those from the Yuan dynasty and earlier. The Japanese mathematicians Yoshida Shichibei Kōyū, Imamura Chishō, and Takahara Kisshu are among the earliest known Japanese mathematicians. They came to be known to their contemporaries as "the Three Arithmeticians".^[4]^[5]

Yoshida was the author of the oldest extant Japanese mathematical text, the 1627 work called Jinkōki. The work dealt with the subject of soroban arithmetic, including square and cube root operations.^[6] Yoshida's book significantly inspired a new generation of mathematicians, and redefined the Japanese perception of educational enlightenment, which was defined in the Seventeen Article Constitution as "the product of earnest meditation".^[7]

Seki Takakazu founded enri (円理: circle principles), a mathematical system with the same purpose as calculus at a similar time to calculus's development in Europe. However Seki's investigations did not proceed from the same foundations as those used in Newton's studies in Europe.^[8]

Mathematicians like Takebe Katahiro played an important role in developing Enri (" circle principle"), a crude analog to the Western calculus.^[9] He obtained power series expansion of $(\arcsin(x))^{2}$ in 1722, 15 years earlier than Euler. He used Richardson extrapolation in 1695, about 200 years earlier than Richardson.^[10] He also computed 41 digits of π, based on polygon approximation and Richardson extrapolation.^[11]

Select mathematicians

The following list encompasses mathematicians whose work was derived from wasan.

Yoshida Mitsuyoshi (1598–1672)
Seki Takakazu (1642–1708)
Takebe Kenkō (1664–1739)
Matsunaga Ryohitsu (fl. 1718-1749)^[12]
Kurushima Kinai (d. 1757)
Arima Raido (1714–1783)^[13]
Fujita Sadasuke (1734-1807)^[14]
Ajima Naonobu (1739–1783)
Aida Yasuaki (1747–1817)
Sakabe Kōhan (1759–1824)
Fujita Kagen (1765–1821)^[14]
Hasegawa Ken (c. 1783-1838)^[13]
Wada Nei (1787–1840)
Shiraishi Chochu (1796–1862)^[15]
Koide Shuke (1797–1865)^[13]
Omura Isshu (1824–1871)^[13]

Notes

^ Selin, Helaine. (1997). Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures, p. 641. , p. 641, at Google Books
^ Smith, David et al. (1914). A History of Japanese Mathematics, p. 1 n2., p. 1, at Google Books
^ Smith, pp. 1–6., p. 1, at Google Books
^ Smith, p. 35. , p. 35, at Google Books
^ Campbell, Douglas et al. (1984). Mathematics: People, Problems, Results, p. 48.
^ Restivo, Sal P. (1984). Mathematics in Society and History, p. 56., p. 56, at Google Books
^ Strayer, Robert (2000). Ways of the World: A Brief Global History with Sources. Bedford/St. Martins. p. 7. ISBN 9780312489168. OCLC 708036979.
^ Smith, pp. 91–127., p. 91, at Google Books
^ Mathematical Society of Japan, Takebe Prize
^ Osada, Naoki (Aug 26, 2011). "収束の加速法の歴史 : 17世紀ヨーロッパと日本の加速法 (数学史の研究)" (PDF). Study of the History of Mathematics RIMS Kôkyûroku (in Japanese). 1787: 100–102 – via Kyoto University.
^ Ogawa, Tsugane (May 13, 1997). "円理の萌芽 : 建部賢弘の円周率計算 : (数学史の研究)" (PDF). Study of the History of Mathematics RIMS Kôkyûroku (in Japanese). 1019: 80–88 – via Kyoto University.
^ Smith, pp. 104, 158, 180., p. 104, at Google Books
^ ^a ^b ^c ^d List of Japanese mathematicians -- Clark University, Dept. of Mathematics and Computer Science
^ ^a ^b Fukagawa, Hidetoshi et al. (2008). Sacred Mathematics: Japanese Temple Geometry, p. 24.
^ Smith, p. 233., p. 233, at Google Books

References

Campbell, Douglas M. and John C. Iggins. (1984). Mathematics: People, Problems, Results. Belmont, California: Warsworth International. ISBN 9780534032005; ISBN 9780534032012; ISBN 9780534028794; OCLC 300429874
Endō Toshisada (1896). History of mathematics in Japan (日本數學史, Dai Nihon sūgakush). Tōkyō: _____. OCLC 122770600
Fukagawa, Hidetoshi, and Dan Pedoe. (1989). Japanese temple geometry problems = Sangaku. Winnipeg: Charles Babbage. ISBN 9780919611214; OCLC 474564475
__________ and Dan Pedoe. (1991) How to resolve Japanese temple geometry problems? (日本の幾何ー何題解けますか?, Nihon no kika nan dai tokemasu ka) Tōkyō. ISBN 9784627015302; OCLC 47500620
__________ and Tony Rothman. (2008). Sacred Mathematics: Japanese Temple Geometry. Princeton: Princeton University Press. ISBN 069112745X; OCLC 181142099
Horiuchi, Annick. (1994). Les Mathematiques Japonaises a L'Epoque d'Edo (1600–1868): Une Etude des Travaux de Seki Takakazu (?-1708) et de Takebe Katahiro (1664–1739). Paris: Librairie Philosophique J. Vrin. ISBN 9782711612130; OCLC 318334322
__________. (1998). "Les mathématiques peuvent-elles n'être que pur divertissement? Une analyse des tablettes votives de mathématiques à l'époque d'Edo." Extrême-Orient, Extrême-Occident, volume 20, pp. 135–156.
Kobayashi, Tatsuhiko. (2002) "What kind of mathematics and terminology was transmitted into 18th-century Japan from China?", Historia Scientiarum, Vol.12, No.1.
Kobayashi, Tatsuhiko. Trigonometry and Its Acceptance in the 18th-19th Centuries Japan.
Ogawa, Tsukane. "A Review of the History of Japanese Mathematics". Revue d'histoire des mathématiques 7, fascicule 1 (2001), 137-155.
Restivo, Sal P. (1992). Mathematics in Society and History: Sociological Inquiries. Dordrecht: Kluwer Academic Publishers. ISBN 9780792317654; OCLC 25709270
Selin, Helaine. (1997). Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures. Dordrecht: Kluwer/Springer. ISBN 9780792340669; OCLC 186451909
David Eugene Smith and Yoshio Mikami. (1914). A History of Japanese Mathematics. Chicago: Open Court Publishing. OCLC 1515528; see online, multi-formatted, full-text book at archive.org

External links

Japan Academy, Collection of native Japanese mathematics
JapanMath, Math program focused on Math Fact Fluency and Japanese originated logic games
Sangaku
Sansu Math, translated Tokyo Shoseki Japanese math curriculum
Kümmerle, Harald. Bibliography on traditional mathematics in Japan (wasan)

[1] Selin, Helaine. (1997). Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures, p. 641. , p. 641, at Google Books

[2] Smith, David et al. (1914). A History of Japanese Mathematics, p. 1 n2., p. 1, at Google Books

[3] Smith, pp. 1–6., p. 1, at Google Books

[smith35-4] Smith, p. 35. , p. 35, at Google Books

[5] Campbell, Douglas et al. (1984). Mathematics: People, Problems, Results, p. 48.

[6] Restivo, Sal P. (1984). Mathematics in Society and History, p. 56., p. 56, at Google Books

[7] Strayer, Robert (2000). Ways of the World: A Brief Global History with Sources. Bedford/St. Martins. p. 7. ISBN 9780312489168. OCLC 708036979.

[8] Smith, pp. 91–127., p. 91, at Google Books

[msj_takebe-9] Mathematical Society of Japan, Takebe Prize

[10] Osada, Naoki (Aug 26, 2011). "収束の加速法の歴史 : 17世紀ヨーロッパと日本の加速法 (数学史の研究)" (PDF). Study of the History of Mathematics RIMS Kôkyûroku (in Japanese). 1787: 100–102 – via Kyoto University.

[11] Ogawa, Tsugane (May 13, 1997). "円理の萌芽 : 建部賢弘の円周率計算 : (数学史の研究)" (PDF). Study of the History of Mathematics RIMS Kôkyûroku (in Japanese). 1019: 80–88 – via Kyoto University.

[12] Smith, pp. 104, 158, 180., p. 104, at Google Books

[clark-13] List of Japanese mathematicians -- Clark University, Dept. of Mathematics and Computer Science

[fukagawa24-14] Fukagawa, Hidetoshi et al. (2008). Sacred Mathematics: Japanese Temple Geometry, p. 24.

[15] Smith, p. 233., p. 233, at Google Books

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