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.
