Implement a Shape abstract class

To learn more about OOP, @nhgrif challenged me to implement a Shape abstract class (more details in code remarks below. Here is how I did it. Any and all advice appreciated!

Shape.java

/* nhgrif says:
 * Phrancis ready for inheritance/polymorphism?
 * Given the following abstract class:
 *
 *  public abstract class Shape {
 *      public abstract double area();
 *      public abstract double perimeter();
 *  }
 *
 * Implement a Circle, Triangle, and Rectangle class which extend the class Shape.
 * Ex: public class Circle extends Shape ... etc
 */

public abstract class Shape {
    public abstract double area();
    public abstract double perimeter();
}

Rectangle.java

public class Rectangle extends Shape {
    private final double width, length; //sides

    public Rectangle() {
        this(1,1);
    }
    public Rectangle(double width, double length) {
        this.width = width;
        this.length = length;
    }

    @Override
    public double area() {
        // A = w * l
        return width * length;
    }

    @Override
    public double perimeter() {
        // P = 2(w + l)
        return 2 * (width + length);
    }

}

Circle.java

public class Circle extends Shape {
    private final double radius;
    final double pi = Math.PI;

    public Circle() {
        this(1);
    }   
    public Circle(double radius) {
        this.radius = radius;
    }

    @Override
    public double area() {
        // A = π r^2
        return pi * Math.pow(radius, 2);
    }

    public double perimeter() {
        // P = 2πr
        return 2 * pi * radius;
    }
}

Triangle.java

```
public class Triangle extends Shape {
private final double a, b, c; // sides

public Triangle() {
this(1,1,1);
}
public Triangle(double a, double b, double c) {
this.a = a;
this.b = b;
this.c = c;
}

@Override
public double area() {
// Heron's formula:
// A = SquareRoot(s (s - a) (s - b)

I am generally impressed with the consistency of the implementations, neatness, etc.

I have a comment about the basic premise. The Shape should not be an abstract class, but an interface. It has no concrete implementations for any methods, and making it an abstract class makes it hard to inherit from other places too. Consider this instead:

public interface Shape {
    public double area();
    public double perimeter();
}

In addition to that concern, the following are also things you should consider:

-
The pi field on your Circle class should be private. There's no need to re-expose an already public constant in another way.

-
I would avoid the 'unit' default constructors. They don't help with anything. When would someone want to call new Triangle() and not want to have the dimensions?

-
Your classes are missing a toString() method. These are useful for many reasons, especially debugging.

-
You don't have a plan for out-of-bound dimensions. What will you do with negative, NaN, or infinite input?

StackExchange Code Review Q#83769, answer score: 21