|New Mexico Supercomputing Challenge|
Challenge Team Abstract
Georges Buffon demonstrated that if you drop many needles on a ruled sheet of paper, and each needle is as long as the distance between the rulings, then the ratio of the number of times that the needles cross a line to the number of times that the needles are dropped slowly approaches 2/pi. There are better ways of calculating pi, but there are many physical situations where this kind of numerical integration, called a Monte Carlo experiment, is the only practical way to solve a problem.
We will implement simulations of Buffon's experiment in C++ using standard pseudo-random number generators and confirm the expected 1/ sqrt(N) rate of convergence, where N is the number of needles thrown. Then we will experiment with several quasi-random number generators in order to identify those which approach the correct result at a 1/N convergence rate.
Pseudo-random numbers are determined sequences of numbers that have as many properties of truly random numbers as possible. Quasi-random numbers are similar sequences, except that they cover the range of allowed numbers in a more regular manner and do not duplicate values. Examples of quasi-random numbers are the fractional parts of multiples of the square root of a small prime and the reversed binary representations of the positive numbers.
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