In fact, it is this extra 7/10ths of an inch, and the fact that it doesn’t fit into standard North American filing systems that have been a major impediment to metrification of paper in North America.
So, what is the logic of metric paper sizing?
First, when metric sizing was being devised, it was decided that scalability among the various sizes would be part of the implementation. This means that ASPECT RATIO, the ratio of the length to the width, would always be the same. (Aspect ratio can be either Length over Width or Width over Length; I’ll use Length over Width in this post.) North Americans trying to scale something formatted for letter (11x8.5”) up tabloid (17x11”) or down the opposite way, have been vexed by the fact that there will either be some wasted white space or elongation or compression in one dimension due to the different aspect ratios. Letter sized has an aspect ratio of 11/8.5 = 1.294 whereas tabloid has an aspect ratio of 17/11 = 1.545.
A few years before the French Revolution, over 200 years ago, Georg Christoph Lichtenberg, a German scientist, noted that paper with an aspect ratio of √2 (=1.4142…) would allow any page to be folded in half and the resulting folded sheet would have the same aspect ratio of 1.4142. (In fact, √2 is sometimes referred to as the Lichtenberg Ratio.)
Shortly after the First War, another German scientist, Dr. Walter Porstmann, developed a formal system of metric based paper sizes. The starting point was a sheet of paper with an area of one square meter with an aspect ratio of √2 or 1189x841mm, rounded to the nearest millimetre. This was designated A0, read as “A-zero”. Folding this in half once results in a sheet half the size but retaining the same aspect ratio of √2, called A1. Folding an A1 in half once results in a sheet half the size (1/4 m2) but retaining the same aspect ratio of √2, called A2. Here is a table of the A-series paper sizes:
So where does B5, used in the Deskfax, fit in? Every B-sized page has an area that is √2 times larger than the A-sized bearing the same number. Thus, Area(B5) = Area(A5) x √2 and Area(A4) = Area(B5) x √2. This puts the B-series papers half-way between adjacent A-sized paper sizes.
In the “Files” section of the blog, there is a new file called “Paper Size Diagrams” that illustrates the various paper sizes, including the different planner page sizes. Download the docx version or the pdf version
Thank you Alan for your excellent explanations.