Takebe Katahiro

Takebe Katahiro, also known as Takebe Kenko, lived from 1664 to 1739 and was a Japanese mathematician and cartographer of the Edo period. He was the favorite 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 the shogun Yoshimune honored him with rank and successively better positions. His new map of Japan, completed in 1719, was highly valued for its quality and detail. He played a critical role in the development of enri, the circle principle, a crude analogue of Western calculus, and he created charts for trigonometric functions. In 1722 he obtained a power series expansion of the square of arcsin x, fifteen years earlier than Euler, and he used Richardson extrapolation in 1695, about two hundred years before Richardson. He also computed 41 digits of pi, and the Mathematical Society of Japan established the Takebe Prize in his name.