6.2 Solutions

    1.  
      void plusEquals (Fraction other)
{
   num = num * other.den + other.num * den;
   den = den * other.den;
}
    2.  
      Fraction plus (Fraction f)
{
   Fraction sum = new Fraction();
   sum.num = num * f.den + f.num * den;
   sum.den = den * f.den;
   return sum;
}
    3.  
      void reduce ()
{
   int min = min(abs(num), abs(den));
   for (int i = min; i > 1; i--)
      if (num % i == 0 && den % i == 0)
      {
         num /= i;
         den /= i;
      }
}
    1.  
      double modulus ()
{
   return abs(sqrt(re*re + im*im));
}
    2.  
      void scale (double x)
{
   re *= x;
   im *= x;
}
    1.  
      Complex plus (Complex c)
{
   Complex sum = new Complex();
   sum.re = re + c.re;
   sum.im = im + c.im;
   return sum;
}
    2.  
      Complex times (Complex c)
{
   Complex product = new Complex();
   product.re = re*c.re - im*c.im;
   product.im = re*c.im + im*c.re;
   return product;
}
    1.  
      double area ()
{
   return PI*r*r;
}
    2.  
      Circle smaller (Circle c)
{
   if (this.area() <= c.area())
      return this;
   else
      return c;
}
    3.  
      boolean isInside (Circle c)
{
   double centreSeparation = sqrt((x-c.x)*(x-c.x) + (y-c.y)*(y-c.y));
   if (centreSeparation + r < c.r)
      return true;
   else
      return false;
}
  5.  
     void setup ()
{
   // Part (a)
   Circle c1 = new Circle();
   c1.x = 4;
   c1.y = -1;
   c1.r = 3;
   Circle c2 = new Circle();
   c2.x = 3;
   c2.y = -2;
   c2.r = 5;
   // Part (b)
   println(c1.area());
   // Part (c)
   Circle small = c1.smaller(c2);
   println("Smaller circle has centre: "
                       + "(" + small.x + "," + small.y
                       + ") and radius " + small.r);
   // Part (d)
   if (c2.isInside(c1))
      println("c2 lies entirely within c1.");
   else
      println("c2 does not lie entirely within c1.");
}