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 pseudorandom 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 quasirandom number generators in order to identify those which approach the correct result at a 1/N convergence rate. Pseudorandom numbers are determined sequences of numbers that have as many properties of truly random numbers as possible. Quasirandom 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 quasirandom numbers are the fractional parts of multiples of the square root of a small prime and the reversed binary representations of the positive numbers. Team Members Sponsoring Teachers Project Advisor(s)
