Transmission delay

2013-10-21T17:37:55Z

14.96.38.90:

{{Japanese name|Takebe}}

{{nihongo|'''Takebe Katahiro'''|建部賢弘||1664 - August 24, 1739}}, also known as '''Takebe Kenkō''', was a [[Japan]]ese [[mathematician]] in 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 [[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"/>

[[Shogun]] [[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>

==Legacy==
Takebe played 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 obtained power series expansion of (arcsin(x))^2 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 [[Richardson extrapolation]], about 200 years earlier than Richardson.

He also computated 41 digits of <math>\pi </math>, based on polygon approximation and Richardson extrapolation.

===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 1o+ 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]] (''[[wasan]]'')
* [[Richardson extrapolation]]

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

==References ==
* Endō Toshisada (1896). {{nihongo|''History of mathematics in Japan''|日本數學史史 |Dai Nihon sūgakush}}. Tōkyō: _____. [http://www.worldcat.org/title/dai-nihon-sugakushi-history-of-mathematics-in-japan-by-endo-toshisada/oclc/122770600&referer=brief_results OCLC 122770600]
* Horiuchi, Annick. (1994). [http://books.google.com/books?id=qMnZHUSAYzMC&dq=History+of+Mathematics+in+Japan+1896&lr=lang_ja&as_brr=0&source=gbs_navlinks_s ''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. 10-ISBN 2711612139/13-ISBN 9782711612130; [http://www.worldcat.org/title/mathematiques-japonaises-a-lepoque-dedo-1600-1868-une-etude-des-travaux-de-seki-takakazu-1708-et-de-takebe-katahiro-1664-1739/oclc/318334322 OCLC 318334322]
* [[Helaine Selin|Selin, Helaine]], ed. (1997). [http://books.google.com/books?id=raKRY3KQspsC&dq=Aida+Yasuaki&source=gbs_navlinks_s ''Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures.''] Dordrecht: [[Kluwer]]/[[Springer Science+Business Media|Springer]]. 10-ISBN 0792340663/13-ISBN 9780792340669; [http://www.worldcat.org/title/encyclopaedia-of-the-history-of-science-technology-and-medicine-in-non-western-cultures/oclc/186451909 OCLC 186451909]
* [[David Eugene Smith]] and [[Yoshio Mikami]]. (1914). [http://books.google.com/books?id=J1YNAAAAYAAJ&dq=Shiraishi+Chochu&source=gbs_navlinks_s ''A History of Japanese Mathematics.''] Chicago: Open Court Publishing. [http://www.worldcat.org/title/history-of-japanese-mathematics/oclc/1515528 OCLC 1515528] [http://www.archive.org/details/historyofjapanes00smitiala -- note alternate online, full-text copy at archive.org]
* {{MacTutor Biography|id=Takebe|title=Takebe Katahiro}}

{{Persondata
| NAME = Takebe Kenko
| ALTERNATIVE NAMES =
| SHORT DESCRIPTION = Mathematician
| DATE OF BIRTH = 1664
| PLACE OF BIRTH =
| DATE OF DEATH = August 24, 1739
| PLACE OF DEATH =
}}
{{DEFAULTSORT:Takebe, Kenko}}
[[Category:Japanese mathematics]]
[[Category:Japanese mathematicians]]
[[Category:17th-century mathematicians]]
[[Category:18th-century mathematicians]]
[[Category:Japanese writers of the Edo period]]
[[Category:18th-century Japanese people]]
[[Category:18th-century cartographers]]

formulasearchengine - User contributions [en]

Transmission delay