In this program it is illustrated the use of  Montecarlo methods  to calculate areas. It is possible to check the results that you get with the well-known values of some simple geometrical figures. It is allowed to change the number of  the randomly generated points as well as the size of the figures.

Here is the applet:

• The vertical scroll bar handles the size of the figure. The exact value of the area is kept in the variable 'a'  and you can see it at the right.
• The number of points the simulation works with is controlled by the horizontal Scroll bar and its value is assigned to 'n'.
• From Figure list you can choose the shape of the geometrical figure.
• Once you have picked out the figure,  the size and the number of points you are interested in, press the Run button to run the program.
• The program shows the points generated and prints two values: the number of points that are inside the figure, m,  and the area, A, calculated from the relation between  m and n.