From the Excellent Book Werner Krauth- February 11, 2005

“Introduction To Monte Carlo Algorithms”, we get some significant issues about how to use random numbers and games to evaluate complicated integrals and describe complex phenomena.

We read…

The word “Monte Carlo method” can be traced back to a game very popular

in Monaco. It’s not what you think, it’s mostly a children’s pass-time played

on the beaches. On Wednesdays (when there is no school) and on weekends,

they get together, pick up a big stick, draw a circle and a square as shown in

figure. They fill their pockets with pebbles 1. Then they stand around, close their eyes, and throw the pebbles randomly in the direction of the square. Someone keeps track of the number of pebbles which hit the square,

and which fall within the circle (see figure). You will easily verify that

the ratio of pebbles in the circle to the ones in the whole square should come

out to be π/4, so there is much excitement when the 40th, 400th, 4000th is

going to be cast.

This breath-taking game is the only method I know to compute the number

π to arbitrary precision without using fancy measuring devices (meter,

balance) or advanced mathematics (division, multiplication, trigonometry).

Children in Monaco can pass the whole afternoon at this game. You are

invited 2 to write a little program to simulate the game. If you have never

written a Monte Carlo program before, this will be your first one.