A Monte Carlo simulator, also known as Monte Carlo methods, is a type of computational method found in a variety of fields ranging from physics to finance.
Monte Carlo simulators use randomized sampling repeatedly in order to obtain a result for a particular mathematical question.
The name is derived from the city of Monte Carlo in Monaco. The origin of the name comes from Manhattan project participants Stanislaw Ulam and John Von Neumann in reference to a relative of Ulam who had a taste for gambling.
Calculating П is an example of a problem especially suited to this type of algorithm and an early example of this is Buffon's needle. You can read more about the history of this experiment at Wolfram MathWorld:
http://mathworld.wolfram.com/BuffonsNeedleProblem.html
In order to calculate П we can also use another method that involves a diagram displaying a circle located in a square divided into four quarters.
In this diagram we are interested in the top-right quarter of...