Author: Rauf Aliev

Somehow I managed to miss this back in the day, but it turned out that the European paper sizes A0, A1, A2, A3, A4, … are not just arbitrary. Let’s start with the fact that A0 has an area of exactly 1 square meter. Well, with a slight error margin to avoid dealing with fractional millimeters. And the aspect ratio — 1:√2 is the only possible one that maintains itself when the paper is divided in half. Thus, there is a rationale behind paper formats in Europe.

But with our paper formats, there seems to be no sense. What we have are letter, legal, tabloid, all with different proportions, and the origin of the format goes back to tradition and is not well known.

I decided to dig into the topic and found a claim that “dimension originates from the days of manual papermaking and that the 11-inch length of the page is about a quarter of ‘the average maximum stretch of an experienced vatman’s arms’. However, the claim does not explain the proportions, but then there is the word vatman, which reminds one of Whatman sheets, remember those? But no, a vatman is a specialist who scooped up the liquid paper pulp from a vat using a mold (sieve) and formed the sheet. And the Whatman sheet comes from James Whatman, an English paper manufacturer of the 18th century, which was simplified to ‘vatman’. Interestingly, the term ‘vatman’ seems to exist only in Russian, derived from Whatman’s surname and his paper, Whatman paper.

And why do we call the formats in the U.S. legal and letter? This is quite interesting as well.

Interestingly, in the U.S., there were two different “standard” sizes initially: 8″ x 10.5″ and 8.5″ x 11″. Different committees independently adopted different standards: 8″ x 10.5″ for the government, and 8.5″ x 11″ for everyone else. When the committees discovered a few years later that they had different standards, they agreed to “disagree until the early 1980s when Reagan finally declared 8.5″ x 11” the officially approved standard size for paper.

The matter began in 1921, when the first Director of the Bureau of the Budget, with the President’s approval, formed an inter-agency advisory group called the “Permanent Conference on Printing,” which approved 8″ x 10½” as the standard format for government agency forms. This continued a practice established earlier by former President Hoover (who was then serving as Secretary of Commerce), defining 8″ x 10½” as the standard format for his department’s forms.

In the same year, the Committee on the Simplification of Paper Sizes, comprising representatives from the printing industry, was appointed to work with the Bureau of Standards as part of Hoover’s program to eliminate waste in industry. This committee defined basic sizes for different types of printed and writing paper. The “writing” size was set as a sheet of 17″ x 22″, while the “legal” size was 17″ x 28″. The now well-known Letter format emerged as a result of dividing these sheets in half (8½” x 11″ and 8½” x 14″).

Even when choosing 8½” x 11″, there wasn’t a special analysis conducted to verify that this size was optimal for commercial forms. The committee that developed these formats aimed solely to “reduce leftovers and waste during the trimming of sheets by reducing the range of paper sizes.”

Moreover, the legal size is still in full use as its name suggests, especially among lawyers, and folders and desk drawers are made to fit its size.

But if you look at a pack of paper in the U.S., you will see “20lb” on the pack. Actually, 20lb is the weight of a small dog, but it is also written that there are 500 pages. “Amazon Basics Multipurpose Copy Printer Paper, 20 Pound, White, 96 Brightness, 8.5 x 11 Inch, 1 Ream, 500 Sheets Total”

In the U.S., the “weight category” of paper indicates the total weight of one ream (500 sheets) of paper in its uncut (original) format. For office paper of the Bond class (often sold in Letter format), the base size is considered to be 17 x 22 inches. For example, a “20-pound” label means that 500 sheets of exactly 17 x 22 weigh 20 pounds. But if we take a pack of Letter format (8.5 x 11), which results from cutting 17 x 22 into four parts, its weight will be about 5 pounds.

In Europe, the weight category essentially refers to the weight of an A0 sheet in grams.

So, if you fold A0 in half, you get A1 with half a square meter area, if you fold A1, you get A2. That’s clear. But how many times can you actually fold a sheet of paper?

The maximum number of times a non-compressible material can be folded has been calculated. With each fold, a part of the paper “loses” for the next potential fold. The function of folding paper in half in one direction is:

L=πt/6(2ⁿ+4)(2ⁿ-1)

where L is the minimum paper length (or other material),

t is the thickness of the material,

n is the number of possible folds.

The length L and thickness t must be expressed in the same units.

The thickness W is calculated as πt2^(3(n-1)/2).

This formula was derived by Britney Gallivan, a high school student from California, in December 2001. In January 2002, she and her helpers spent eight hours folding a roll of toilet paper about 4000 feet long (approximately 1200 meters) twelve times in the same direction, thus debunking the old myth that paper cannot be folded more than eight times.

Sources mention that she started in school with gold foil (I wrote about such foil recently), and, starting with a square sheet the size of a hand, after many hours of perseverance and practice, using rulers, soft brushes, and tweezers, she managed to fold her gold foil twelve times. But apparently, that wasn’t spectacular enough, and she found toilet paper over a kilometer long somewhere in 2002 and made a show for the Guinness record.

Britney didn’t stop there and wrote a book. Though it was only 48 pages. How about that, Britney?