郝成春的个人主页 | Chengchun HAO's Homepage

研究员、博士生导师，中国科学院数学与系统科学研究院 数学研究所 | Professor, Institute of Mathematics, AMSS, CAS

**中科院数学与系统科学研究院**

**数学研究所**

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**偏微分方程研讨班**

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#### 题目/Title: Random approximations of $\pi$

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.

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