the Golden Ratio and the Fibonacci series (Perl program)

I've been re-reading Dan Brown's The Da Vinci Code lately, and I was intrigued by the Golden Ratio and how it relates to the Fibonacci series. The Fibonacci series is such that each term is the sum of the previous two terms:
1, 1, 2, 3, 5, 8, 13, ...

The ratio of consecutive terms in the Fibonacci series converges on the Golden Ratio, which has a value of approximately 1.618. It also shows up in a geometric analysis of the pentacle. These properties are discussed in mathematical detail on the following Web pages:

the Golden Ratio
pentacle geometry

I wanted to see this from a computational point of view, so I wrote a quick Perl program to compute the Fibonacci numbers and ratios out to around 100 terms. The program prints out deviations from the Golden Ratio, and the output shows a near-zero deviation after less than 40 terms.

#!/usr/bin/perl -w

use strict;
use diagnostics;

my $NUM_ITERATIONS = 100;
my $GOLDEN_RATIO = 0.5 * (1.0 + sqrt(5));

my ($previous_term, $current_term) = (1, 1);
my $iteration_number = 1;
while ( $iteration_number <= $NUM_ITERATIONS ) {
    my $new_term = $previous_term + $current_term;
    my $ratio = $new_term / $current_term;
    my $deviation = abs($GOLDEN_RATIO-$ratio) / $GOLDEN_RATIO;
    printf "% 3d: %e\n", $iteration_number, $deviation;
    $previous_term = $current_term;
    $current_term = $new_term;
    $iteration_number++;
}