# Takebe Kenkō

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.[1]

## Biography

Takebe was the favorite student of the Japanese mathematician Seki Takakazu[1] Takebe is considered to have extended and disseminated Seki's work.[2]

In 1706, Takebe was offered a position in the Tokugawa shogunate's department of ceremonies.[1]

In 1719, Takebe's new map of Japan was completed; and the work was highly valued for its quality and detail.[1]

Shōgun Yoshimune honored Takebe with rank and successively better positions in the shogunate.[3]

## Legacy

Takebe played critical role in the development of the Enri (円理, "circle principle") - a crude analogon to the western calculus. He also created charts for trigonometric functions.[4]

He obtained power series expansion of ${\displaystyle (\arcsin(x))^{2}}$ 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 ${\displaystyle \pi }$, 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.[4]

## 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.[5]