Calculating PI approximation with Java

Question

I'm trying to write a code that approximates the value of PI. What I'm doing is:

• drawing a circle inside a rectangle

• drawing random points inside the rectangle and circle

• calculating the ratio between rect/cicle

• calculating 4/ratio

• that should be PI

This my code:

import java.awt.Color;
import java.awt.Frame;
import java.awt.Graphics;
import java.awt.Point;
import java.awt.event.WindowAdapter;
import java.awt.event.WindowEvent;
import java.util.ArrayList;
import java.util.Random;

public class Main extends Frame {

    int width = 800;
    ArrayList<Point> list = new ArrayList<Point>();


    public void points(Graphics g) {
        int numPoint = 10000000;

        for (int i = 0; i < numPoint; i++) {

            int min = 23;
            int max = 23 + width;
            Random rand = new Random();

            int x = rand.nextInt(width);
            int y = (int) (Math.random() * (max - min + 1) + min);
            Point temp = new Point(x, y);
            list.add(temp);
            if (inCircle(temp)) {
                g.setColor(Color.green);
            } else {
                g.setColor(Color.blue);
            }
            g.drawLine(x, y, x, y);
        }
    }


    public void paint(Graphics g) {
        g.fillRect(0, 0, 1000, 1000);
        int x = width / 2;
        int y = width / 2 + 23;
        int radius = width / 2;
        g.setColor(Color.WHITE);
        g.drawOval(x - radius, y - radius, radius * 2, radius * 2);
        g.drawRect(0, 23, width, width);
        points(g);
        calculatingPI();
    }


    public void calculatingPI() {
        double inCircle = 0;
        double inRect = list.size();
        for (Point p : list) {
            if (inCircle(p)) {
                inCircle++;
            }
        }
        double ratio = inRect / inCircle;
        System.out.print("PI is approximated to: " + 4 / ratio + "  ");
    }


    public boolean inCircle(Point p) {
        Point center = new Point(width / 2, width / 2 + 23);
        return center.distance(p) <= width / 2;
    }
    

    public static void main(String[] args) {
        Frame frame = new Main();
        frame.addWindowListener(new WindowAdapter() {
            public void windowClosing(WindowEvent we) {
                System.exit(0);
            }
        });
        // circle coordinates.
        frame.setSize(800, 1000);
        frame.setVisible(true);
    }
} 

It works quite fine, even if most of the time the number is around 1,13 which is not a great approx.

The question is: The more I decrease the size of the rectangle and circle, (without changing the number of points), the less PI becomes accurate. I don't understand, why is that? Is there a problem in my code?

Shouldn't it be the opposite? The smallest the area, the more points are accurate, the more PI is accurate. Why is isn't it the case?

Answer 1

You are using integer pixels. This means the smaller you make your "circle", the worse it approximates a true circle. For example here's the circle within a 3x3 pixel square: it does not look circular at all.

 █ 
███
 █ 

To get a better approximation, use double floating point numbers instead of integers. Use Point2D.Double instead of the Point class:

ArrayList<Point2D.Double> list = new ArrayList<>();

To generate the random points:

double x = Math.random() * width;
double y = Math.random() * (max - min) + min;
Point2D.Double temp = new Point2D.Double(x, y);

Note that where you had max-min+1 , the +1 has to be removed.

To test if the point is within the circle:

public boolean inCircle(Point2D.Double p) {
    Point2D.Double center = new Point2D.Double(width / 2d, width / 2d + 23);
    return center.distance(p) <= width / 2d;
}