Overview Monte Carlo method

monte carlo method applied approximating value of π. after placing 30,000 random points, estimate π within 0.07% of actual value.

monte carlo methods vary, tend follow particular pattern:

for example, consider circle inscribed in unit square. given circle , square have ratio of areas π/4, value of π can approximated using monte carlo method:

in procedure domain of inputs square circumscribes circle. generate random inputs scattering grains on square perform computation on each input (test whether falls within circle). finally, aggregate results obtain our final result, approximation of π.

there 2 important points: firstly, if grains not uniformly distributed, approximation poor. secondly, there should large number of inputs. approximation poor if few grains randomly dropped whole square. on average, approximation improves more grains dropped.

uses of monte carlo methods require large amounts of random numbers, , use spurred development of pseudorandom number generators, far quicker use tables of random numbers had been used statistical sampling.