【摘要】 本文应用数论方法解决一个实际中遇到的单位圆的覆盖问题。用单位圆上的均匀布点方法估计覆盖面积S的均值、方差及其分布函数,结果显示Beta分布可以较好的拟合S/π的分布。为了增大覆盖面积,推荐采用序贯方法安排随机圆,模拟结果显示序贯方法非常有效。本文还指出了序贯方法在加权单位圆的覆盖问题中效果也显著。更多还原

【Abstract】 In this paper,number theoretic method is used to solve a practical problem,i.e.,the coverage problem of unit circle.The uniform design in unit circle is used to estimate the mean,variance and distribution of coverage area S.It is shown that Beta distribution can be approximated to the distribution of S/π.For increasing the coverage area,the sequential method is suggested to arrange the random circles,and the simulation results show this method is very useful.Moreover,the sequential method is also efficient in the coverage problem of weighted unit circle.更多还原