'Allow Math.PI as a reference to the PI constant' means that your code will have to look like this in order to work:

static double getCircumference(double radius ) {
      return Math.PI * 2 * radius;
 }
 public static double getArea(double radius) {
      return Math.PI * radius * radius;
 }

What import java.lang.Math; does is importing the class java.lang.Math so you can reference it with Math instead of the qualified version java.lang.Math. import java.lang.Math.*; does the same for Math and all nested classes, but not it's members.

Here is usage of Math.PI to find circumference of circle and Area First we take Radius as a string in Message Box and convert it into integer

public class circle {

    public static void main(String[] args) {
        // TODO code application logic here

        String rad;

        float radius,area,circum;

       rad = JOptionPane.showInputDialog("Enter the Radius of circle:");

        radius = Integer.parseInt(rad);
        area = (float) (Math.PI*radius*radius);
        circum = (float) (2*Math.PI*radius);

        JOptionPane.showMessageDialog(null, "Area: " + area,"AREA",JOptionPane.INFORMATION_MESSAGE);
        JOptionPane.showMessageDialog(null, "circumference: " + circum, "Circumfernce",JOptionPane.INFORMATION_MESSAGE);
    }

}

What you want to do is print out the raw bit pattern for the PI values and compare them.

In Java use the http://java.sun.com/j2se/1.5.0/docs/api/java/lang/Double.html#doubleToRawLongBits(double) method to get the long value that you should print as binary.

Java 5 gives:

• PI is 3.141592653589793
• Raw bits is 4614256656552045848
• Binary is 100000000001001001000011111101101010100010001000010110100011000

In C, you can do double pi = M_PI; printf("%lld\n", pi); to obtain the same 64bit integer: 4614256656552045848 (thanks Bruno).

If it could vary by the instance of a class, then it's clearly not a constant. What would it mean to get a different value of pi for each instance of Math (not that Math even allows instances to be constructed)? Or a different case insensitive ordering for each instance of String?

I would highly advise against having a single constants class. It may seem a good idea at the time, but when developers refuse to document constants and the class grows to encompass upwards of 500 constants which are all not related to each other at all (being related to entirely different aspects of the application), this generally turns into the constants file being completely unreadable. Instead:

• If you have access to Java 5+, use enums to define your specific constants for an application area. All parts of the application area should refer to enums, not constant values, for these constants. You may declare an enum similar to how you declare a class. Enums are perhaps the most (and, arguably, only) useful feature of Java 5+.
• If you have constants that are only valid to a particular class or one of its subclasses, declare them as either protected or public and place them on the top class in the hierarchy. This way, the subclasses can access these constant values (and if other classes access them via public, the constants aren't only valid to a particular class...which means that the external classes using this constant may be too tightly coupled to the class containing the constant)
• If you have an interface with behavior defined, but returned values or argument values should be particular, it is perfectly acceptible to define constants on that interface so that other implementors will have access to them. However, avoid creating an interface just to hold constants: it can become just as bad as a class created just to hold constants.