This experiment was based on this Reddit posting: http://www.reddit.com/r/fifthworldproblems/comments/s0217/i_can_only_speak_in_a_recurring_meter_the/c4a4c18

Here’s a brief excerpt that sums up the point of this experiment:

Cool fact:

The Fibonacci sequence fairly accurately converts miles to kilometers. For each number in the sequence that represents miles, the next number is the same distance in kilometers

Wanting to test this, I threw together a quick Perl script to plot this out. The results were, surprisingly, “fairly accurate.”

I’ve included here a few quick plots, the numbers, and the raw source code should anyone wish to tinker further with this. Granted these are unrefined results from a presentation stand-point, but you get the point…

The raw results:

Miles, Calculated from Fibonacci, True

1,1,1.609

1,2,1.609

2,3,3.218

3,5,4.827

5,8,8.045

8,13,12.872

13,21,20.917

21,34,33.789

34,55,54.706

55,89,88.495

Miles, Percent Difference

1,-37.8495960223741

1,24.3008079552517

2,-6.77439403356122

3,3.58400662937643

5,-0.559353635798632

8,0.994406463642015

13,0.396806425395604

21,0.624463582822808

34,0.537418199100641

55,0.570653709249105

89,0.557956997507005

144,0.562806436019613

233,0.560954075386042

377,0.561661608360142

610,0.561391353961833

987,0.561494581832304

1597,0.561455152276278

2584,0.561470213023878

4181,0.561464460329799

6765,0.561466657663354

10946,0.561465818356607

17711,0.561466138943263

28657,0.561466016490064

46368,0.561466063263029

75025,0.561466045397334

121393,0.561466052221422

196418,0.561466049614862

317811,0.561466050610479

514229,0.56146605023018

832040,0.561466050375433

The source code:

Perl |copy code |?

001 002 `#!/usr/bin/perl`

003 004 use GD::Graph::lines;005 006 `##################`

007 `# Computed values`

008 009 $last = 1;010 $cur = 1;011 my @a;012 013 print "Miles, Calculated from Fibonacci, True\n";014 015 for ($i = 0; $i < 10; $i++) {016 $a[0][$i] = $last; #miles017 $a[1][$i] = $cur; # Fibonacci Calculated value018 $a[2][$i] = $last * 1.609; # computed value019 print $a[0][$i] . "," . $a[1][$i] . "," . $a[2][$i] . "\n";020 021 `# increment the Fibonacci sequence`

022 $x = $cur; $cur += $last; $last = $x;023 `}`

024 025 my $mygraph = GD::Graph::lines->new(600, 400);026 $mygraph->set(027 x_label => 'Miles',028 y_label => 'Kilometers',029 title => 'Miles to Kilometers',030 ) or warn $mygraph->error;031 032 my $myimage = $mygraph->plot(\@a) or die $mygraph->error;033 open OUTPUT, ">Fib_vs_KM.png";034 print OUTPUT $myimage->png;035 close(OUTPUT);036 037 `#################`

038 `# % Error 1 - 55`

039 040 print "\nMiles, Percent Difference\n";041 042 $last = 1;043 $cur = 1;044 my @a;045 046 for ($i = 0; $i < 10; $i++) {047 $a[0][$i] = $last; #miles048 $a[1][$i] = ($cur - ($last * 1.609)) / ($last * 1.609) * 100; # percent difference049 050 print $a[0][$i] . "," . $a[1][$i] . "\n";051 `# increment the Fibonacci sequence`

052 $x = $cur; $cur += $last; $last = $x;053 `}`

054 055 my $mygraph = GD::Graph::lines->new(600, 400);056 $mygraph->set(057 x_label => 'Miles',058 y_label => '% Difference',059 title => 'Percent Difference from Real (1 - 55 miles)',060 ) or warn $mygraph->error;061 062 my $myimage = $mygraph->plot(\@a) or die $mygraph->error;063 open OUTPUT, ">Fib_vs_KM_diff1.png";064 print OUTPUT $myimage->png;065 close(OUTPUT);066 067 `############`

068 `# 89 - 6765`

069 070 for ($i = 0; $i < 10; $i++) {071 $a[0][$i] = $last; #miles072 $a[1][$i] = ($cur - ($last * 1.609)) / ($last * 1.609) * 100; # percent difference073 print $a[0][$i] . "," . $a[1][$i] . "\n";074 075 `# increment the Fibonacci sequence`

076 $x = $cur; $cur += $last; $last = $x;077 `}`

078 079 my $mygraph = GD::Graph::lines->new(600, 400);080 $mygraph->set(081 x_label => 'Miles',082 y_label => '% Difference',083 title => 'Percent Difference from Real (89 - 6765 miles)',084 ) or warn $mygraph->error;085 086 my $myimage = $mygraph->plot(\@a) or die $mygraph->error;087 open OUTPUT, ">Fib_vs_KM_diff2.png";088 print OUTPUT $myimage->png;089 close(OUTPUT);090 091 092 `#################`

093 `# 10946 - 832040`

094 095 for ($i = 0; $i < 10; $i++) {096 $a[0][$i] = $last; #miles097 $a[1][$i] = ($cur - ($last * 1.609)) / ($last * 1.609) * 100; # percent difference098 print $a[0][$i] . "," . $a[1][$i] . "\n";099 100 `# increment the Fibonacci sequence`

101 $x = $cur; $cur += $last; $last = $x;102 `}`

103 104 my $mygraph = GD::Graph::lines->new(600, 400);105 $mygraph->set(106 x_label => 'Miles',107 y_label => '% Difference',108 title => 'Percent Difference from Real (10946 - 832040 miles)',109 ) or warn $mygraph->error;110 111 my $myimage = $mygraph->plot(\@a) or die $mygraph->error;112 open OUTPUT, ">Fib_vs_KM_diff3.png";113 print OUTPUT $myimage->png;114 close(OUTPUT);115