Okay I got my last assignment about calculating the square root, but this assignment just has me really confused. I'm not sure how I'm suppose to use Monte Carlo's method. Here's what I have to do.
Imagine that the square dart board has a coordinate system attached to it. The upper right corner has coordinates ( 1.0, 1.0) and the lower left corner has coordinates ( -1.0, -1.0 ). It has sides that are 2 units long and its center (as well as the center of the inscribed circle) is at the origin.
A random point inside the dart board can be specified by its x and y coordinates. These values are generated using the random number generator. There is a method nextDouble() that will return a double between 0.0 (inclusive) and 1.0 (exclusive). But we need random numbers between -1.0 and +1.0. The way we achieve that is:
double xPos = (randomGen.nextDouble()) * 2 - 1.0;
double yPos = (randomGen.nextDouble()) * 2 - 1.0;
To determine if a point is inside the circle its distance from the center of the circle must be less than the radius of the circle. The distance of a point with coordinates ( xPos, yPos ) from the center is Math.sqrt ( xPos * xPos + yPos * yPos ). The radius of the circle is 1 unit.
In your method main() you want to experiment and see if the accuracy of PI increases with the number of throws on the dartboard. You will compare your result with the value given by Math.PI. The quantity Difference in the output is your calculated value of PI minus Math.PI. Use the following number of throws to run your experiment - 100, 1000, 10,000, and 100,000. You will call the method computePI() with these numbers as input parameters. Your output will be of the following form:
Computation of PI using Random Numbers
Number of throws = 100, Computed PI = ..., Difference = ...
Number of throws = 1000, Computed PI = ..., Difference = ...
Number of throws = 10000, Computed PI = ..., Difference = ...
Number of throws = 100000, Computed PI = ..., Difference = ...
* Difference = Computed PI - Math.PI
In the method computePI() you will simulate the throw of a dart by generating random numbers for the x and y coordinates. You will call the method isInside() to determine if the point is inside the circle or not. This you will do as many times as specified by the number of throws. You will keep a count of the number of times a dart landed inside the circle. That figure divided by the total number of throws is the ratio π / 4. The method computePI() will return the computed value of PI.
So this is what I have so far..I know the structure of the program...I just don't know how to actually make it.
CODE
import java.util.Random;
public class CalculatePI
{
public static boolean isInside ( double xPos, double yPos )
{
double xPos = (randomGen.nextDouble()) * 2 - 1.0;
double yPos = (randomGen.nextDouble()) * 2 - 1.0;
}
public static double computePI ( int numThrows )
{
}
public static void main ( String[] args )
{
Random randomGen = new Random ( System.currentTimeMillis() );
}
}
Any suggestions on what I should do next? or add... or take out?
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