Application of Monte Carlo method in the simulation of circumference ratio

摘要

We have calculated the circumference ratio by Monte Carlo method and Buffon's Needle algorithm. Our results reveal that the estimated value approaches to the expected value as the Monte Carlo steps increase. The error between the estimated and the expected values decreases inversely as the square root of MCS increases. When MCS reaches 1010, the error is only one part per million of the expected value.