{{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'' 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>
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==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] * 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] * 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. {{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 the Edo period