View source for Takebe Kenkō

{{short description|Japanese mathematician and cartographer}}
{{family name hatnote|Takebe|lang=Japanese}}

{{nihongo|'''Takebe Katahiro'''|建部 賢弘||1664 – August 24, 1739}}, also known as '''Takebe Kenkō''', was a Japanese mathematician and cartographer during the [[Edo period]].<ref name="smith146">Smith, David. (1914). {{Google books|J1YNAAAAYAAJ|''A History of Japanese Mathematics,'' p. 146. |page=146}}</ref>

==Biography==
Takebe was the favorite student of the Japanese mathematician [[Seki Takakazu]]<ref name="smith146"/> Takebe is considered to have extended and disseminated Seki's work.<ref>[http://www.britannica.com/eb/article-9384143/Takebe-Katahiro "Takebe Katahiro", ''Encyclopædia Britannica'' online.]</ref>

In 1706, Takebe was offered a position in the [[Tokugawa shogunate]]'s department of ceremonies.<ref name="smith146"/>

In 1719, Takebe's new map of Japan was completed; and the work was highly valued for its quality and detail.<ref name="smith146"/>

''[[Shōgun]]'' [[Tokugawa Yoshimune|Yoshimune]] honored Takebe with rank and successively better positions in the shogunate.<ref>Jochi, Shigeru. (1997). "Takebe Katahiro," {{Google books|raKRY3KQspsC&dq|''Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures'', p. 932. |page=932}}</ref>

{{Pi box}}

==Legacy==
Takebe played a critical role in the development of the [[Enri]] ({{lang|ja-Hani|円理}}, "circle principle") - a crude analogon to the western [[calculus]].   He also created charts for trigonometric functions.<ref name="msj_takebe">[http://mathsoc.jp  Mathematical Society of Japan], [http://mathsoc.jp/en/pamph/current/takebe_pr.html  Takebe Prize]</ref>

He achieved a [[power series]] expansion of <math>(\arcsin(x))^2</math> in 1722, 15 years earlier than Euler.
This was the first power series expansion obtained in Wasan.  This result was first conjectured by heavy numeric computation.

He used the [[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 <math>\pi</math>, based on polygon approximation and the 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>

===Takebe Prizes===
In the context of its 50th anniversary celebrations, the [[Mathematical Society of Japan]] established the Takebe Prize and the Takebe Prizes for the encouragement of young people who show promise as mathematicians.<ref name="msj_takebe"/>

==Selected works==
In a statistical overview derived from writings by and about Takebe Kenko, [[OCLC]]/[[WorldCat]] encompasses roughly 10+ works in 10+ publications in 3 languages and 10+ library holdings.<ref>[http://www.oclc.org/research/activities/identities/default.htm  WorldCat Identities]: [http://www.worldcat.org/identities/lccn-nr2004-22449  建部賢弘 1664-1739]</ref>
{{dynamic list}}
* 1683 – {{nihongo|''Kenki sanpō''|研幾算法}} [http://www.worldcat.org/search?q=no:%22056510086%22  OCLC 22056510086]
* 1685 – {{nihongo|''Hatsubi sanpō endan genkai''|發微算法演段諺解}} [http://www.worldcat.org/search?q=no:%22056085721%22  OCLC 22056085721]

==See also==
* [[Sangaku]], the custom of presenting mathematical problems, carved in wood tablets, to the public in [[shinto shrines]]
* [[Soroban]], a Japanese [[abacus]]
* [[Japanese mathematics]]
* [[Richardson extrapolation]]

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

==References ==
* Endō Toshisada (1896). {{nihongo|''History of mathematics in Japan''|大日本數學史|Dai Nihon sūgakushi}}. Tōkyō: _____. [https://www.worldcat.org/oclc/122770600  OCLC 122770600]
* [[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]
* [[Helaine Selin|Selin, Helaine]], ed. (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 -- note alternate online, full-text copy at archive.org]
* {{MacTutor Biography|id=Takebe|title=Takebe Katahiro}}

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{{DEFAULTSORT:Takebe, Kenko}}
[[Category:1664 births]]
[[Category:1739 deaths]]
[[Category:17th-century Japanese mathematicians]]
[[Category:18th-century cartographers]]
[[Category:18th-century Japanese mathematicians]]
[[Category:Writers of Edo-period Japan]]