Japanese Mathematics

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## History

## Select mathematicians

## See also

## Notes

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This article uses material from the Wikipedia page available here. It is released under the Creative Commons Attribution-Share-Alike License 3.0.

Japanese Mathematics

**Japanese mathematics** (, *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 ( *y?san*).^{[2]}

In the history of mathematics, the development of *wasan* falls outside the Western realms of people, propositions and alternate solutions.^{[clarification needed]} 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*.

This mathematical schema evolved during a period when Japan's people were isolated from European influences. Kambei Mori is the first Japanese mathematician noted in history.^{[3]} Kambei is known as a teacher of Japanese mathematics; and among his most prominent students were Yoshida Shichibei K?y?, Imamura Chish?, and Takahara Kisshu. These students came to be known to their contemporaries as "the Three Arithmeticians".^{[4]}

Yoshida was the author of the oldest extant Japanese mathematical text. The 1627 work was named *Jink?ki*. The work dealt with the subject of soroban arithmetic, including square and cube root operations.^{[5]} 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".^{[6]}

Seki Takakazu founded *enri* (: circle principles), a mathematical system with the same purpose as calculus at a similar time to calculus's development in Europe; but Seki's investigations did not proceed from conventionally shared foundations^{[clarification needed]}.^{[7]}

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

- Kambei Mori (early 17th century)
- Yoshida Mitsuyoshi (1598-1672)
- Seki Takakazu (1642-1708)
- Takebe Kenk? (1664-1739)
- Matsunaga Ryohitsu (fl. 1718-1749)
^{[8]} - Kurushima Kinai (d. 1757)
- Arima Raido (1714-1783)
^{[9]} - Fujita Sadasuke (1734-1807)
^{[10]} - Ajima Naonobu (1739-1783)
- Aida Yasuaki (1747-1817)
- Sakabe K?han (1759-1824)
- Fujita Kagen (1765-1821)
^{[10]} - Hasegawa Ken (c. 1783-1838)
^{[9]} - Wada Nei (1787-1840)
- Shiraishi Chochu (1796-1862)
^{[11]} - Koide Shuke (1797-1865)
^{[9]} - Omura Isshu (1824-1871)
^{[9]}

- Japanese theorem for cyclic polygons
- Japanese theorem for cyclic quadrilaterals
- Sangaku, the custom of presenting mathematical problems, carved in wood tablets, to the public in Shinto shrines
- Soroban, a Japanese abacus
- Category:Japanese mathematicians

**^**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**^**Campbell, Douglas*et al.*(1984).*Mathematics: People, Problems, Results,*p. 48.**^**Smith,*p. 35.*, p. 35, at Google Books**^**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**^**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

- Campbell, Douglas M. and John C. Iggins. (1984).
*Mathematics: People, Problems, Results.*Belmont, California: Warsworth International. ISBN 9780534032005; ISBN 9780534032012; ISBN 9780534028794; OCLC 300429874 - End? Toshisada (1896).
*History of mathematics in Japan*(,*Dai Nihon s?gakush*). T?ky?: _____. 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?*(,*Nihon no kika nan dai tokemasu ka*) T?ky? : Mori Kitashuppan. 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.
- Morimoto, Mitsuo. "Infinite series in Japanese Mathematics of the 18th Century".
- Morimoto, Mitsuo. "A Chinese Root of Japanese Traditional Mathematics - Wasan"
- 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

- 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)*

This article uses material from the Wikipedia page available here. It is released under the Creative Commons Attribution-Share-Alike License 3.0.

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