Editing Japanese mathematics (section)

==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>