Spring Semester 2003

Solve problem P6.12 in Big Java p. 278.

Here's the text of the problem:

The Heron method is a method for computing square roots that was known to the ancient Greeks. If x is a guess for the value Math.sqrt(a), then the average of x and a/x is a better guess.

The problem asks to implement a class RootApproximator that starts with an initial guess of 1 and whose nextGuess method produces a sequence of increasingly better guesses. Supply a method hasMoreGuesses that returns false if two successive guesses are sufficiently close to each other. Then test your class like this:

RootApproximator r = new RootApproximator(n); 
while (r.hasMoreGuesses()) 
  System.out.println(r.nextGuess()); 

(Doesn't this look awfully similar to the way we use StringTokenizers?

The above is your Homework Three.

Needless to say you are not allowed to make any use of Math.sqrt(...) in your program.

Traditionally Homework Three was like that.

(However we have since posted a solution, see the link above).

Can you answer that last question though in the posted solution?