quinta-feira, 12 de março de 2015

A Monte Carlo Simulation for Pi Day

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by Joseph Rickert What will you be doing at 26 minutes and 53 seconds past 9 this coming Saturday morning? I will probably be running simulations. I have become obsessed with an astounding result from number theory and have been trying to devise Monte Carlo simulations to get at it. The result, well known to number theorists says: choose two integers at random; the probability that they will be coprime is 6/π2 ! Here, π materializes out of thin air. Who could have possibly guessed this? - well, Leonhard Euler, apparently, and this sort of magic seems to be quite...

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