use strict;
use warnings;

use PDF::API2;

use constant PAGE_WIDTH      => 595;
use constant PAGE_HEIGHT     => 842;

use constant LINE_WIDTH      =>   0.5;
use constant THIN_LINE_WIDTH =>   0.25;
use constant CM              =>  28.346457;  # 1 cm in points

sub log16 {
  my $n = shift;
  return log($n) / log(16);
}

sub angle {
  my $theta = shift;
  return -360.0 * log16($theta)
}

sub run {
  my $pdf = PDF::API2->new;
  my $font = $pdf->corefont("TimesNewRoman");
  $pdf->mediabox(PAGE_HEIGHT, PAGE_WIDTH);
  my $gfx = $pdf->page->gfx;
  $gfx->strokecolor( '#000' );
  $gfx->linewidth( THIN_LINE_WIDTH );

  my $yc = PAGE_WIDTH / 2.0;
  my $radius = PAGE_HEIGHT / 4.0 - 1 * CM;
  my @tick16 = map( $_ / 16.0, (16 .. 255) );

  my %outerDisk =
    (centre => PAGE_HEIGHT / 4.0,
     dir => +1,
     bigLetter => 0.35 * CM,
     smallLetter => 0.18 * CM
    );
  my %innerDisk =
    (centre => 3.0 * PAGE_HEIGHT / 4.0,
     dir => -1,
     bigLetter => -0.6 * CM,
     smallLetter => -0.3 * CM
    );

  for my $disk ( \%outerDisk, \%innerDisk ) {

    $gfx->save();

    $gfx->translate($$disk{centre}, $yc);

    $gfx->linewidth( LINE_WIDTH );
    $gfx->circle(0, 0, 1);
    $gfx->circle(0, 0, $radius);
    $gfx->circle(0, 0, $radius + 0.75 * CM * $$disk{dir});
    $gfx->stroke();

    $gfx->linewidth( THIN_LINE_WIDTH );
    $gfx->move(0, -0.5 * CM);
    $gfx->line(0, 0.5 * CM);
    $gfx->stroke();
    $gfx->move(-0.5 * CM, 0);
    $gfx->line(0.5 * CM, 0);
    $gfx->stroke();

    for my $i (@tick16) {
      my $angle = angle($i);
      $gfx->rotate($angle);
      if ($i * 16 % 16 == 0) {
        $gfx->move(0, $radius);
        $gfx->line(0, $radius + 0.3 * CM * $$disk{dir});
        $gfx->stroke;
        $gfx->textlabel(0, $radius + $$disk{bigLetter}, $font, 10, spr
+intf("%X", $i), -align => 'center');
      }
      elsif ($i * 16 % 4 == 0) {
        $gfx->move(0, $radius);
        $gfx->line(0, $radius + 0.15 * CM * $$disk{dir});
        $gfx->stroke;
      }
      else {
        $gfx->move(0, $radius);
        $gfx->line(0, $radius + 0.1 * CM * $$disk{dir});
        $gfx->stroke;
      }
      if ($i < 4.0 and $i * 16 % 16 != 0) {
        $gfx->textlabel(0, $radius + $$disk{smallLetter}, $font, 5, sp
+rintf("%X", $i * 16 % 16), -align => 'center');
      }
      if ($i > 4.0 and $i < 8.0 and $i * 16 % 2 == 0 and $i * 16 % 16 
+!= 0) {
        $gfx->textlabel(0, $radius + $$disk{smallLetter}, $font, 5, sp
+rintf("%X", $i * 16 % 16), -align => 'center');
      }
      if ($i > 8.0 and $i * 16 % 4 == 0 and $i * 16 % 16 != 0) {
        $gfx->textlabel(0, $radius + $$disk{smallLetter}, $font, 5, sp
+rintf("%X", $i * 16 % 16), -align => 'center');
      }
      $gfx->rotate(-$angle);
    }

    $gfx->restore();

  }

  $pdf->saveas("hex_slide_rule.pdf");
}

run();
[download]

1. Run program and print out resulting pdf.
2. Carefully cut out disks.
3. Put the inner disk over the outer disk with the centres carefully aligned and pin together.