As Long as the Emperor's Foot?

I am most grateful to Karen Reeds for drawing our attention to her brother's Web site about standard paper sizes. It's a subject that has interested me for many years and although I have built up a moderate body of information about it, there is much in Karen's brother's pages that was new to me. I recommend everyone to give the page a visit at

http://www.ft.uni-erlangen.de/~mskuhn/iso-paper.html

What Markus Kuhn does not say is that A4 paper, being 297mm along its longer side is actually the length of an ancient Roman Foot!

As will be generally known among subscribers to Origami-L, the ratio of the sides of papers in the International A and B series is one to the square root of two. (This ratio has been given the name of the Silver Rectangle on the analogy of the Golden Rectangle.) Such paper has the characteristic that if it is folded into half across the width, the resulting half sheet also has the identical ratio. The A series is used much more than the B series, the sizes of which are intermediate between the A sizes. To put it shortly, the largest of the basic A series is A0, with dimensions of 841 X 1189mm. A1 is half that at 594 X 841mm, then A2 at 420 x 594 mm, A3 at 297 X 420, A4 at 210 X 297 and so on. Incidentally, these are not the precise dimensions which would be derived from an exact mathematical calculation. They have been rounded up or down to the nearest millimetre to make the sizes more commercially workable. So don't expect your A4 to be exactly of the ratio one to root two.

How were the dimensions of A0 arrived at? The area of a sheet of A0 (the 0 stands for zero, not the letter O) is one square metre distorted into a shape of the ratio one to root two.

As is generally known, the devisers of the metric system originally calculated the length of a metre as one ten-millionth of the length of a quadrant of of the circumference of the Earth measured from the equator to the pole. With the instruments and techniques of the day, they didn't quite get it right, but the metre was formalised as the length of a metal rod kept in Paris and was later redefined as 1,650,763.73 wavelengths of the orange-red line in the krypton-86 spectrum. (I have often wondered why they didn't take the opportunity of rounding it off a bit! But I expect they had their reasons.)

Subsequently (for Britain at any rate - I don't know whether other English-speaking countries followed suit,) the yard was defined in terms of the metre.

All this is very scientific, so what is all this about the Roman Foot? It must be admitted that it is not easy to be precise about the exact length of a Roman foot measure. However, according to Pliny the Elder, a Roman Stadion had the same length as a Greek Stadion and contained 625 Roman Feet. The Stadion has been calculated at 185 metres, which gives a length of 296.9 millimetres for a Roman foot. I may say, that there are other ways of arriving at a Roman foot, but they all give very approximately the same figure.

So, a Roman Foot at 296.9 millimetres is extremely close to the 297 millimetres of the length of A4 paper. It must be borne in mine that the length of A4, having been rounded up is itself only approximate. But more to the point, in an age when measures varied widely and when measuring techniques and instruments were comparatively primitive, it is very improbable that the ancient Romans were capable of defining their own measures to anything like an accuracy of one tenth of a millimetre.

The conclusion is that A4 is indeed the length of a Roman foot. Now isn't that an extraordinary coincidence? So much so that some people think that the length of A4 was chosen because it was the length of a Roman foot! But if you start at the opposite end with a Roman foot, you still arrive at A0 having the precise area of a square metre.

David Lister.