学术报告：Random approximations of $\pi$

中科院数学与系统科学研究院

数学研究所 

学术报告会

报告人：  徐文青 教授（北京工业大学)

题  目：Random approximations of  $\pi$

时  间：2016.07.12（星期二）, 15:00--16:00

地  点：思源楼 S705

摘要：

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.