Monte Carlo methods use probabilities to make calculations in real life situations.  For example, if you wanted to measure the area of some irregular shapes (e.g. an oil slick), enclose these shapes within a rectangle of know area.  Then pick at random points within that rectangle.  The ratio of points that hit the irregular shapes to the total number of points within the rectangle is then multiplied by the known area of the rectangle to give an approximation of the area of the irregular shapes. 


Questions for research:

Is there a relationship between the number of points used and the accuracy of the results? 

Is there a relationship between the area of the enclosing rectangle of known area and the accuracy of the results?

What is the best way to generate the necessary random points?