中科院数学与系统科学研究院
数学研究所
偏微分方程研讨班
Speaker: Professor Wenqing Xu (Beijing University of Technology)
Title: Random approximations of $\pi$
Time: 3:00-4:00pm, Jul. 12, 2016
Place: Rm. S705, Siyuan Building
Abstract: We present some results on random approximations of $\pi$ by using the semiperimeter or area of a random $n$-sided polygon inscribed in (or circumscribed about) a unit circle in the plane. We show that, with probability 1, the approximation error goes to $0$ as $n$ tends to infinity, and is roughly sextupled when compared with the classical Archimedean approach of using a regular $n$-sided polygon. Furthermore, by combining both the semiperimeter and area of these random polygons, we also construct extrapolation improvements that can significantly speed up the convergence of these approximations.