Watch Newton's method converge

newton.pl

my $square = shift or die "Usage: $0 3 [where 3 is the number you want to find the square root of]";

my $guess;

print 
"This is an implementation of Newton's method for finding roots.
(Specifically, we're finding square roots here, although Newton's
method can be used for many different kinds of functions.)
The only goal is for you to see how rapidly it converges, it is
otherwise quite useless :D.\n\n\n";

print "Ok, we're trying to find the sqare root of [$square].\n\n\n";

while (1) {
    if ($guess) {
        print "Our current guess is [$guess].  Squared, that's ". $guess*$guess .".  So we're off by [". abs( $square - $guess*$guess ) ."]\n";
        my $next_guess = 1/2*($guess + $square/$guess);
        print "By newton's method, our next guess is [". $next_guess . "]\n";
        print "Hit enter when you are ready for the next step: ";
        <>;
        print "\n\n";
        $guess = $next_guess;
    }
    else {
        print "Enter your best guess for the square root! ";
        $guess = <>;
        chomp $guess;
    }
}