Would it not just be a matter of making sure the object was printed to it's
real-life dimensions?  By resizing the photo while having activated the
rulers in your editing software you could do it.

The easiest thing to do is to take a picture of a ruler with the lens
set exactly the same way as in the photograph of the coin and then
enlarge/scale the photograph to match. You could visually match the
coin, but matching the ruler is easier because the ruler will tell
you exactly how much you need to correct from your first attempt.

In the days in which people made life-size images on film to
be contact printed, the method was to set the film plane to
object distance at four times the actual (measured) focal
length of the lens. (This method assumes that the nodal
space of the lens is negligible at full size copying).

While you could theoretically set an exact reduction to
the digital sensor by measurement, this is not likely
to be very practical because you would need to know:
1) the actual focal length of your lens
2) either the position of the nodes of the lens
  or the amount of nodal space.
3) the exact location of the sensor/film plane
  (sometimes marked by a line through a circle)

There are excellent tables of optical formulas
in any edition of the British Journal of Photography
Almanac or in any book on photographic optics.

In practice, taking a picture of a ruler and then
adjusting is likely to be your best option.

Peter.

To make an image at 1:1 (life size) all that you need to do is make the
image on the film/chip exactly the same size as the actual image. That
means that if your subject is 5" long you can not make a 1:1 image in
camera on any camera using film or a chip that is not at least 5" long.

If your camera has too small a capture medium then you would have to
output it so that the image of the object was exactly the same length as
the original.

As for what you will need that is camera specific. On a view camera you
would only need a lens/lensboard and film/chip of the proper size.

On a 35mm type camera or a medium format camera you would also need a
bellows or extension tube set. You could us a close up lens in some
cases but not if you want the best results.

To shoot 1:1 you need a lens extension 2x the focal length of the lens.

If you want to focus 1:1 i.e. to photograph a 24x36mm area on a full
frame 35mm camera, then bellows or extension tubes were usually needed,
however if the lens was pretty good at closest focus then it was a
simple matter of placing the object on the enlarger table and setting
the enlarger to expose at that magnification.

Modern lenses for digital cameras will focus much closer than the old
SLRs - My Fuji S7000 will focus down to about 1cm meaning I could print
a 1c or English penny on paper measuring 33x25cm (bigger than A4) at
300dpi - about 15-20x full size.

Printing actual size, simply resize the canvas to the actual size of the
coin.

Advanced mathematic are unnecessary, just accuracy in measuring the
subject and calculating canvas size.

One way to easily record a coin at full-size is to use a flatbed scanner
- years ago, coin dealers used to photocopy their coins for ads etc.

There are infinitely many ways to do it.  You get to adjust the size
at two steps, once when you take the photo, and again when you make
the print.  So essentially anything you choose at the first step you
can compensate for at the second step (sometimes with consequences) to
get the result you want.

The easiest thing to do is probably to include a ruler in the photo
(in a location where you can crop it out).  Then adjust size in
Photoshop to make an inch on the ruler exactly 300 pixels, and then
print telling the printer to print 300 DPI.  

Larry-

Its math, but not very advanced.  Peter Irwin's suggestion to use a ruler,
is a good idea regardless.

To start, a digital photo itself doesn't have a size, it has pixels.  Your
screen displays so many pixels per inch, resulting in an object having a
certain size on the screen.

Then when you print, the printer has so many pixels per inch, resulting in
an object having a certain size on the printed page that may be different
from that shown on the screen.

With bit-image graphics programs, you might need to do the math.  With
"Draw" programs that use vector-graphics, there is usually a grid on the
screen that indicates the size of an object, including the printed size.
In other words, the program works with the printer driver to ensure the
final image is the specified size.

Examples of such vector graphics programs are Claris Draw, Adobe
Illustrator and the Draw functions of ClarisWorks and AppleWorks.

Fred

A 1:1 macro.

*************************************
A man said to the universe:
"Sir, I exist!"
"However" replied the universe,
"The fact has not created in me
 A sense of obligation."
                  Stephen Crane