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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.

Date icon 2016-06-08