Takebe Kenkō

Takebe Kenkō, also known as Takebe Katahiro (1664 to 1739), was a Japanese mathematician and cartographer of the Edo period. He was the favourite student of the mathematician Seki Takakazu and is considered to have extended and disseminated Seki's work. In 1706 he was offered a position in the Tokugawa shogunate's department of ceremonies, and in 1719 his new map of Japan was completed and highly valued for its quality and detail. Shogun Yoshimune honoured him with rank and successively better posts. He played a critical role in the development of the enri, the circle principle, a crude analogue of Western calculus, and he made charts of trigonometric functions. In 1722 he obtained a power series expansion of the square of arcsin x, fifteen years before Euler, the first such expansion in wasan, and the result was first conjectured by heavy numeric computation. In 1695 he used Richardson extrapolation, about 200 years before Richardson, and he computed 41 digits of pi from polygon approximation with the same technique. The Mathematical Society of Japan established the Takebe Prize in his name.