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Originally Posted by Hitchhiker 42
What is a Monte Carlo simulation?
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https://en.wikipedia.org/wiki/Monte_Carlo_method
Randomly sample the set of all line segments, and find the mean length of only the segments in the sample (a finite number chosen to suit your computational resources, rather than the uncountably infinite number in the entire set). If the sampling matches the probability distribution/weighting of the set, then the law of large numbers says your mean will approach the true mean as sample size increases.