题 目： Random approximations of pi
时 间： 2016年6月10号 11：00－12：00
报告人： 徐文青 教授 (北京工业大学，California State University, Long Beach))
地 点： 蒙民伟楼1105室
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.