Login
Login

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 1870sSelin, Helaine. (1997). {{Google books|raKRY3KQspsC&dq|Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures, p. 641. |page=641}} and employed to distinguish native Japanese mathematical theory from Western mathematics (洋算 yōsan).Smith, David et al. (1914). {{Google books|J1YNAAAAYAAJ|A History of Japanese Mathematics, p. 1 n2.|page=1}}

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}.Smith, {{Google books|J1YNAAAAYAAJ|pp. 1–6.|page=1}}

=Edo period=

Image:Yoshida Soroban.jpg in Yoshida Koyu's Jinkōki (1641 edition)]]

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".Smith, {{Google books|J1YNAAAAYAAJ|p. 35. |page=35}}Campbell, Douglas et al. (1984). Mathematics: People, Problems, Results, p. 48.

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.Restivo, Sal P. (1984). {{Google books|gvMm0jv-xPIC| Mathematics in Society and History, p. 56.|page=56}} 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".{{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}}

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.Smith, {{Google books|J1YNAAAAYAAJ|pp. 91–127.|page=91}}

Mathematicians like Takebe Katahiro played an important role in developing Enri (" circle principle"), an analog to the Western calculus.[http://mathsoc.jp Mathematical Society of Japan], [http://mathsoc.jp/en/pamph/current/takebe_pr.html Takebe Prize] 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.{{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}} He also computed 41 digits of π, based on polygon approximation and Richardson extrapolation.{{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}}

Select mathematicians

File:Seki Kowa Katsuyo Sampo Bernoulli numbers.png and Binomial coefficient.]]

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

{{dynamic list}}

See also

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 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]
  • 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. {{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)]

{{Authority control}}

{{DEFAULTSORT:Japanese Mathematics}}

Mathematics