Takebe Kenkō

Takebe Katahiro (建部 賢弘^?, 1664 – August 24, 1739), also known as Takebe Kenkō, was a Japanese mathematician in the Edo period.

Takebe was the favorite student of Seki Takakazu 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.

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.

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.

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