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

Edo period The , also known as the , is the period between 1600 or 1603 and 1868 in the history of Japan, when the country was under the rule of the Tokugawa shogunate and some 300 regional ''daimyo'', or feudal lords. Emerging from the chaos of the Sengok ...

.Smith, David. (1914).

Biography

Takebe was the favorite student of the Japanese mathematician Seki Takakazu 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, also known as the was the military government of Japan during the Edo period from 1603 to 1868. The Tokugawa shogunate was established by Tokugawa Ieyasu after victory at the Battle of Sekigahara, ending the civil wars ...

'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 rulers 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, except during parts of the Kamak ...

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

Legacy

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

calculus Calculus is the mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations. Originally called infinitesimal calculus or "the ...

. He also created charts for trigonometric functions. Mathematical Society of Japan
/ref> He achieved a

power series In mathematics, a power series (in one variable) is an infinite series of the form \sum_^\infty a_n \left(x - c\right)^n = a_0 + a_1 (x - c) + a_2 (x - c)^2 + \dots where ''a_n'' represents the coefficient of the ''n''th term and ''c'' is a co ...

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 the

Richardson extrapolation In numerical analysis, Richardson extrapolation is a Series acceleration, 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 se ...

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

\pi

, based on polygon approximation and the Richardson extrapolation.

Takebe Prizes

In the context of its 50th anniversary celebrations, the

Mathematical Society of Japan The Mathematical Society of Japan (MSJ, ) is a learned society for mathematics in Japan. In 1877, the organization was established as the ''Tokyo Sugaku Kaisha'' and was the first academic society in Japan. It was re-organized and re-established i ...

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. 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 founded in 1967 as the ...

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 O ...

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 Wolters Kluwer N.V. is a Dutch information services company. The company serves legal, business, tax, accounting, finance, audit, risk, compliance, and healthcare markets. Wolters Kluwer in its current form was founded in 1987 with a merger bet ...

Springer Springer or springers may refer to: Publishers * Springer Science+Business Media, aka Springer International Publishing, a worldwide publishing group founded in 1842 in Germany formerly known as Springer-Verlag. ** Springer Nature, a multinationa ...

.
OCLC 186451909
* David Eugene Smith and Yoshio Mikami. (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 Writers of the Edo period