Calculate the average area of a lune determined by two points uniformly randomly picked in a disk under the condition that the lune contains the origin; see http://math.stackexchange.com/questions/355415.

Question355415.java

public class Question355415 {
    public static void main (String [] args) {
        int ntrials = Integer.parseInt (args [0]);

        double sum = 0;

        double [] [] p = new double [3] [2];

        for (int n = 0;n < ntrials;n++) {
            double d;
            do {
                for (int i = 0;i < 2;i++) {
                    double s;
                    do {
                        s = 0;
                        for (int j = 0;j < 2;j++) {
                            p [i] [j] = 2 * Math.random () - 1;
                            s += p [i] [j] * p [i] [j];
                        }
                    } while (s > 1);
                }
                d = d (p,0,1);
            } while (d < d (p,0,2) || d < d (p,1,2));
            sum += d;
        }

        System.out.println (sum / ntrials);
    }

    static double d (double [] [] p,int i1,int i2) {
        double d = 0;
        for (int j = 0;j < 2;j++) {
            double diff = p [i1] [j] - p [i2] [j];
            d += diff * diff;
        }
        return d;
    }
}