Editing Japanese mathematics

{{Short description|Independent development of mathematics in Japan during the isolation of the Edo period}}
{{nihongo|'''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<ref>[[Helaine Selin|Selin, Helaine]]. (1997). {{Google books|raKRY3KQspsC&dq|''Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures'', p. 641. |page=641}}</ref> and employed to distinguish native Japanese mathematical theory from Western mathematics (洋算 ''yōsan'').<ref>Smith, David ''et al.'' (1914). {{Google books|J1YNAAAAYAAJ|''A History of Japanese Mathematics'', p. 1 n2.|page=1}}</ref>

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 [[Chinese influence on Japanese culture|knowledge from China reached Japan]], including that of [[Kanji#history|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 <math>a^{m}*a^{n} = a^{m + n}</math>.<ref>Smith, {{Google books|J1YNAAAAYAAJ|pp. 1–6.|page=1}}</ref>

===Edo period===
[[Image:Yoshida Soroban.jpg|thumb|The [[soroban]] in [[Yoshida Koyu]]'s ''[[Jinkōki]]'' (1641 edition)]]
The Japanese mathematical [[Model (abstract)|schema]] evolved during a period when Japan's people were isolated from European influences, but instead borrowed from [[Ten Computational Canons|ancient mathematical texts]] written in China, including those from the [[Yuan dynasty]] and earlier. The Japanese mathematicians [[Yoshida Koyu|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".<ref name="smith35">Smith, {{Google books|J1YNAAAAYAAJ|p. 35. |page=35}}</ref><ref>Campbell, Douglas ''et al.'' (1984). ''Mathematics: People, Problems, Results,'' p. 48.</ref>

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.<ref>Restivo, Sal P. (1984). {{Google books|gvMm0jv-xPIC|'' Mathematics in Society and History'', p.  56.|page=56}}</ref> 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|Seventeen Article Constitution]] as "the product of earnest meditation".<ref>{{Cite book|title=Ways of the World: A Brief Global History with Sources|last=Strayer|first=Robert|publisher=Bedford/St. Martins|year=2000|isbn=9780312489168|oclc=708036979|pages=7}}</ref>

[[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.<ref>Smith, {{Google books|J1YNAAAAYAAJ|pp. 91–127.|page=91}}</ref>

Mathematicians like [[Takebe Katahiro]] played an important role in developing Enri (" circle principle"), an analog to the Western calculus.<ref name="msj_takebe">[http://mathsoc.jp  Mathematical Society of Japan], [http://mathsoc.jp/en/pamph/current/takebe_pr.html  Takebe Prize]</ref> He obtained [[power series]] expansion of <math>(\arcsin(x))^2</math> in 1722, 15 years earlier than [[Euler]]. He used [[Richardson extrapolation]] in 1695, about 200 years earlier than Richardson.<ref>{{Cite journal|last=Osada|first=Naoki|date=Aug 26, 2011|title=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)|url=http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/pdf/1787-07.pdf|journal=Study of the History of Mathematics RIMS Kôkyûroku|language=Japanese|volume=1787|pages=100–102|via=Kyoto University}}</ref> He also computed 41 digits of π, based on polygon approximation and Richardson extrapolation.<ref>{{Cite journal|last=Ogawa|first=Tsugane|date=May 13, 1997|title=円理の萌芽 : 建部賢弘の円周率計算 : (数学史の研究)|url=http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/pdf/1019-7.pdf|journal=Study of the History of Mathematics RIMS Kôkyûroku|language=Japanese|volume=1019|pages=80–88|via=Kyoto University}}</ref>

== Select mathematicians ==
[[File:Seki Kowa Katsuyo Sampo Bernoulli numbers.png|thumb|240px|Replica of ''Katsuyo Sampo'' by Seki Takakazu. Page written about [[Bernoulli number]] and [[Binomial coefficient]].]]
The following list encompasses mathematicians whose work was derived from ''wasan.''
{{dynamic list}}
* [[Yoshida Mitsuyoshi]] (1598–1672)
* [[Seki Takakazu]] (1642–1708)<!-- circle principle ([[enri]]) which represents a crude form of integral calculus -->
* [[Takebe Kenkō]] (1664–1739)
* [[Matsunaga Ryohitsu]] ([[floruit|fl.]] 1718-1749)<ref>Smith, {{Google books|J1YNAAAAYAAJ|pp. 104, 158, 180.|page=104}}</ref>
* [[Kurushima Kinai]] (d. 1757)
* [[Arima Raido]] (1714–1783)<ref name="clark">[http://aleph0.clarku.edu/~djoyce/mathhist/japan.html  List of Japanese mathematicians] -- [[Clark University]], <!-- David E. Joyce --> [http://aleph0.clarku.edu/~djoyce/mathhist/mathhist.html   Dept. of Mathematics and Computer Science]</ref>
* [[Fujita Sadasuke]] (1734-1807)<ref name="fukagawa24">Fukagawa, Hidetoshi ''et al.'' (2008). ''[[Sacred Mathematics: Japanese Temple Geometry]]'', p. 24.</ref>
* [[Ajima Naonobu]] (1739–1783)
* [[Aida Yasuaki]] (1747–1817)
* [[Sakabe Kōhan]] (1759–1824)
* [[Fujita Kagen]] (1765–1821)<ref name="fukagawa24"/>
* [[Hasegawa Ken]] (c. 1783-1838)<ref name="clark"/>
* [[Wada Nei]] (1787–1840)
* [[Shiraishi Chochu]] (1796–1862)<ref>Smith, {{Google books|J1YNAAAAYAAJ| p. 233.|page=233}}</ref>
* [[Koide Shuke]] (1797–1865)<ref name="clark"/>
* [[Omura Isshu]] (1824–1871)<ref name="clark"/>

==See also==
* [[Japanese theorem for cyclic polygons]]
* [[Japanese theorem for cyclic quadrilaterals]]
* [[Hungarian mathematics]]
* [[Sangaku]], the custom of presenting mathematical problems, carved in wood tablets, to the public in [[Shinto shrines]]
* [[Soroban]], a Japanese [[abacus]]
* [[:Category:Japanese mathematicians]]

==Notes==
{{reflist|2}}

== References ==
* Campbell, Douglas M. and John C. Iggins. (1984). [https://books.google.com/books?id=z6xFAAAAYAAJ&q=Kambei+Mori   ''Mathematics: People, Problems, Results.''] Belmont, California: Warsworth International. {{ISBN|9780534032005}}; {{ISBN|9780534032012}}; {{ISBN|9780534028794}}; [https://www.worldcat.org/oclc/300429874   OCLC 300429874]
* Endō Toshisada (1896). {{nihongo|''History of mathematics in Japan''|日本數學史  |Dai Nihon sūgakush}}. Tōkyō: _____. [https://www.worldcat.org/oclc/122770600  OCLC 122770600]
* Fukagawa, Hidetoshi, and [[Daniel Pedoe|Dan Pedoe]]. (1989).  ''Japanese temple geometry problems = Sangaku''. Winnipeg: Charles Babbage. {{ISBN|9780919611214}}; [https://www.worldcat.org/oclc/474564475   OCLC 474564475]
* __________ and Dan Pedoe. (1991) {{nihongo|''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}}; [https://www.worldcat.org/oclc/47500620   OCLC 47500620]
* __________ and [[Tony Rothman]]. (2008). ''[[Sacred Mathematics: Japanese Temple Geometry]]''. Princeton: [[Princeton University Press]]. {{ISBN|069112745X}}; [https://www.worldcat.org/oclc/181142099   OCLC 181142099]
* [[Annick Horiuchi|Horiuchi, Annick]]. (1994). [https://books.google.com/books?id=qMnZHUSAYzMC&q=History+of+Mathematics+in+Japan+1896   ''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}}; [https://www.worldcat.org/oclc/318334322   OCLC 318334322]
*  __________. (1998). [http://www.persee.fr/doc/oroc_0754-5010_1998_num_20_20_1059 "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. [http://www.mi.sanu.ac.rs/vismath/visbook/kobayashi/index.html Trigonometry and Its Acceptance in the 18th-19th Centuries Japan].
* Ogawa, Tsukane. "[http://smf4.emath.fr/Publications/RevueHistoireMath/7/pdf/smf_rhm_7_137-155.pdf A Review of the History of Japanese Mathematics]". ''Revue d'histoire des mathématiques'' '''7''', fascicule 1 (2001), 137-155.
* Restivo, Sal P. (1992). [https://books.google.com/books?id=gvMm0jv-xPIC&q=Yoshida+Koyu+arithmetic  ''Mathematics in Society and History: Sociological Inquiries.''] Dordrecht: Kluwer Academic Publishers. {{ISBN|9780792317654}}; [https://www.worldcat.org/oclc/25709270   OCLC 25709270]
* Selin, Helaine. (1997). [https://books.google.com/books?id=raKRY3KQspsC&q=Aida+Yasuaki   ''Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures.''] Dordrecht: [[Kluwer]]/[[Springer Science+Business Media|Springer]]. {{ISBN|9780792340669}}; [https://www.worldcat.org/oclc/186451909   OCLC 186451909]
* [[David Eugene Smith]] and [[Yoshio Mikami]]. (1914). [https://books.google.com/books?id=J1YNAAAAYAAJ&q=Shiraishi+Chochu   ''A History of Japanese Mathematics.''] Chicago: Open Court Publishing. [https://www.worldcat.org/oclc/1515528   OCLC 1515528]; [https://archive.org/details/historyofjapanes00smitiala  ''see'' online, multi-formatted, full-text book at archive.org]

==External links==
* Japan Academy, [http://www.japan-acad.go.jp/en/about/material.html  Collection of native Japanese mathematics]
* JapanMath, [http://www.japanmath.com  Math program focused on Math Fact Fluency and Japanese originated logic games]
*[http://www.wasan.jp/english/index.html Sangaku]
*Sansu Math, [http://www.koyopublishing.com  translated Tokyo Shoseki Japanese math curriculum]
* Kümmerle, Harald. [http://hkuemmerle.de/blog/index.php/bibliography-traditional-mathematics/ ''Bibliography on traditional mathematics in Japan (wasan)'']

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[[Category:Japanese mathematics| ]]
[[Category:Science and technology in Japan|Mathematics]]