Takebe Kenko
Encyclopedia
, also known as Takebe Kenkō, was a Japan
ese mathematician
in the Edo period
.
Takebe is considered to have extended and disseminated Seki's work.
In 1706, Takebe was offered a position in the Tokugawa shogunate
'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.
Shogun
Yoshimune
honored Takebe with rank and successively better positions in the shogunate.
. He also created charts for trigonometric functions.
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
.
He also computated 41 digits of
, based on polygon approximation and Richardson extrapolation.
established the Takebe Prize and the Takebe Prizes for the encouragement of young people who show promise as mathematicians.
/WorldCat
encompasses roughly 10+ works in 1o+ publications in 3 languages and 10+ library holdings.
Japan
Japan is an island nation in East Asia. Located in the Pacific Ocean, it lies to the east of the Sea of Japan, China, North Korea, South Korea and Russia, stretching from the Sea of Okhotsk in the north to the East China Sea and Taiwan in the south...
ese mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
in the Edo period
Edo period
The , or , is a division of Japanese history which was ruled by the shoguns of the Tokugawa family, running from 1603 to 1868. The political entity of this period was the Tokugawa shogunate....
.
Biography
Takebe was the favorite student of Seki TakakazuSeki Takakazu
, also known as , was a Japanese mathematician in the Edo period.Seki laid foundations for the subsequent development of Japanese mathematics known as wasan; and he has been described as Japan's "Newton."...
Takebe is considered to have extended and disseminated Seki's work.
In 1706, Takebe was offered a position in the Tokugawa shogunate
Tokugawa shogunate
The Tokugawa shogunate, also known as the and the , was a feudal regime of Japan established by Tokugawa Ieyasu and ruled by the shoguns of the Tokugawa family. This period is known as the Edo period and gets its name from the capital city, Edo, which is now called Tokyo, after the name was...
'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.
Shogun
Shogun
A was one of the hereditary military dictators of Japan from 1192 to 1867. In this period, the shoguns, or their shikken regents , were the de facto rulers of Japan though they were nominally appointed by the emperor...
Yoshimune
Tokugawa Yoshimune
was the eighth shogun of the Tokugawa shogunate of Japan, ruling from 1716 until his abdication in 1745. He was the son of Tokugawa Mitsusada, the grandson of Tokugawa Yorinobu, and the great-grandson of Tokugawa Ieyasu.-Lineage:...
honored Takebe with rank and successively better positions in the shogunate.
Legacy
Takebe played critical role in the development of the Enri - a crude analogon to the western calculusCalculus
Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem...
. He also created charts for trigonometric functions.
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
Richardson extrapolation
In numerical analysis, Richardson extrapolation is a sequence acceleration method, used to improve the rate of convergence of a sequence. It is named after Lewis Fry Richardson, who introduced the technique in the early 20th century. In the words of Birkhoff and Rota, ".....
.
He also computated 41 digits of
, based on polygon approximation and Richardson extrapolation.Takebe Prizes
In the context of its 50th anniversary celebrations, the Mathematical Society of JapanMathematical Society of Japan
The Mathematical Society of Japan was the first academic society in Japan.In 1877, the organization was establisehd as the Tokyo Sugaku Kaisha. It was re-organized and re-established in its present form in 1946....
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, OCLCOCLC
OCLC Online Computer Library Center, Inc. is "a nonprofit, membership, computer library service and research organization dedicated to the public purposes of furthering access to the world’s information and reducing information costs"...
/WorldCat
WorldCat
WorldCat is a union catalog which itemizes the collections of 72,000 libraries in 170 countries and territories which participate in the Online Computer Library Center global cooperative...
encompasses roughly 10+ works in 1o+ publications in 3 languages and 10+ library holdings.
- 1683 — OCLC 22056510086
- 1685 — OCLC 22056085721
See also
- SangakuSangakuSangaku or San Gaku are Japanese geometrical puzzles in Euclidean geometry on wooden tablets which were placed as offerings at Shinto shrines or Buddhist temples during the Edo period by members of all social classes.-History:The Sangaku were painted in color on wooden tablets and hung in the...
, the custom of presenting mathematical problems, carved in wood tablets, to the public in shinto shrines - SorobanSorobanThe is an abacus developed in Japan. It is derived from the Chinese suanpan, imported from China via Korea to Japan around 1600. Like the suanpan, the soroban is still used today, despite the proliferation of practical and affordable pocket electronic calculators....
, a Japanese abacusAbacusThe abacus, also called a counting frame, is a calculating tool used primarily in parts of Asia for performing arithmetic processes. Today, abaci are often constructed as a bamboo frame with beads sliding on wires, but originally they were beans or stones moved in grooves in sand or on tablets of... - Japanese mathematicsJapanese mathematicsdenotes a distinct kind of mathematics which was developed in Japan during the Edo Period . The term wasan, from wa and san , was coined in the 1870s and employed to distinguish native Japanese mathematics theory from Western mathematics .In the history of mathematics, the development of wasan...
(wasan) - Richardson extrapolationRichardson extrapolationIn numerical analysis, Richardson extrapolation is a sequence acceleration method, used to improve the rate of convergence of a sequence. It is named after Lewis Fry Richardson, who introduced the technique in the early 20th century. In the words of Birkhoff and Rota, ".....