Takebe played a critical role in the development of the
Enri (, "circle principle") - a crude analogon to the western
calculus. He also created charts for trigonometric functions. He achieved a
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 the
Richardson extrapolation in 1695, about 200 years earlier than Richardson. He also computed 41 digits of \pi, based on polygon approximation and the 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. ==Selected works==