, also known as Takebe Kenkō, was a Japanese mathematician and cartographer during the

Edo period The or is the period between 1603 and 1867 in the history of Japan, when Japan was under the rule of the Tokugawa shogunate and the country's 300 regional '' daimyo''. Emerging from the chaos of the Sengoku period, the Edo period was characteriz ...

.Smith, David. (1914).

Biography

Takebe was the favorite student of the Japanese mathematician

Seki Takakazu , Selin, Helaine. (1997). ''Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures,'' p. 890 also known as ,Selin, was a Japanese mathematician and author of the Edo period. Seki laid foundations for the subs ...

Takebe is considered to have extended and disseminated Seki's work. In 1706, Takebe was offered a position in the

Tokugawa shogunate The Tokugawa shogunate (, Japanese 徳川幕府 ''Tokugawa bakufu''), also known as the , was the military government of Japan during the Edo period from 1603 to 1868. Nussbaum, Louis-Frédéric. (2005)"''Tokugawa-jidai''"in ''Japan Encyclopedia ...

's department of ceremonies. In 1719, Takebe's new map of Japan was completed; and the work was highly valued for its quality and detail. ''

Shōgun , officially , was the title of the military dictators of Japan during most of the period spanning from 1185 to 1868. Nominally appointed by the Emperor, shoguns were usually the de facto rulers of the country, though during part of the Kamakur ...

'' Yoshimune honored Takebe with rank and successively better positions in the shogunate.

Legacy

Takebe played critical role in the development of the Enri (, "circle principle") - a crude analogon to the western

calculus Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithm ...

. He also created charts for trigonometric functions. Mathematical Society of Japan
/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 In numerical analysis, Richardson extrapolation is a sequence acceleration method used to improve the rate of convergence of a sequence of estimates of some value A^\ast = \lim_ A(h). In essence, given the value of A(h) for several values of h, we ...

in 1695, about 200 years earlier than Richardson. He also computated 41 digits of

\pi

, 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.

Selected works

In a statistical overview derived from writings by and about Takebe Kenko,

OCLC OCLC, Inc., doing business as OCLC, See also: is an American nonprofit cooperative organization "that provides shared technology services, original research, and community programs for its membership and the library community at large". It was ...

WorldCat WorldCat is a union catalog that itemizes the collections of tens of thousands of institutions (mostly libraries), in many countries, that are current or past members of the OCLC global cooperative. It is operated by OCLC, Inc. Many of the OCL ...

encompasses roughly 10+ works in 10+ publications in 3 languages and 10+ library holdings. WorldCat Identities 建部賢弘 1664-1739
/ref> * 1683 –
OCLC 22056510086
* 1685 –
OCLC 22056085721

Notes

References

* Endō Toshisada (1896). . Tōkyō: _____
OCLC 122770600
* Horiuchi, Annick. (1994)
''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.
OCLC 318334322
* Selin, Helaine, ed. (1997)
''Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures.''
Dordrecht: Kluwer/ Springer.
OCLC 186451909
* David Eugene Smith and

Yoshio Mikami was a Japanese mathematician and historian of ''Japanese mathematics''. He was born February 16, 1875, in Kotachi, Hiroshima prefecture. He attended the High School of Tohoku University, and in 1911 was admitted to the Imperial University of Tok ...

. (1914)
''A History of Japanese Mathematics.''
Chicago: Open Court Publishing
OCLC 1515528-- note alternate online, full-text copy at archive.org
* {{DEFAULTSORT:Takebe, Kenko 1664 births 1739 deaths 17th-century Japanese mathematicians 18th-century cartographers 18th-century Japanese mathematicians Japanese writers of the Edo period