1. Why Paper with a 1:√2 Ratio Keeps Its Shape When Cut in Half
On October 25, 1786, the German scholar Lichtenberg wrote a letter to his friend Beckmann. He noted that if the ratio of the short side to the long side is 1:√2, you can fold the paper and keep the same shape. He mentioned that the writing paper he had on hand already had this property [1]. The number √2 is approximately 1.414. It is the ratio of the side of a square to its diagonal. A rectangle with this ratio, when cut in half along the long side, produces two pieces that have the same ratio [2]. A0 paper has an area of 1 square meter. Each time you cut it in half, the number increases: A1, A2, and so on [2].
It is important to note that Lichtenberg did not create the standard. He was simply someone who noticed the property of the paper and wrote it down. The German standard DIN 476 for paper with a √2 ratio appeared in 1921. It became the international standard ISO 216 in 1975, according to encyclopedia entries [3]. But can this "clean paper" alone explain the books on Japanese shelves?
2. How Old Books Got Their Sizes by Folding Large Sheets of Paper
In the era of letterpress printing, books were made by printing multiple pages on the front and back of one large sheet of paper, then folding and binding it. Therefore, the size of the book was determined by the size of the original paper and how many times it was folded. Old paper was made by hand [7].
The name of the book format changes based on the number of folds. Folding one sheet once creates 2 leaves (4 pages), called Folio. Folding it twice creates 4 leaves (8 pages), called Quarto. Folding it three times creates 8 leaves, called Octavo [7]. With the same size paper, more folds mean a smaller book. If you look up the name Shiroku-ban, you can see this connection.
3. Why Japan's B Sizes for Books Differ from the International B Sizes
If you measure common book sizes, A5 is 148 × 210 mm, B5 is 182 × 257 mm, and B6 is 128 × 182 mm [4]. If you divide the height by the width, 210 ÷ 148 is about 1.42, and 257 ÷ 182 is about 1.41. Both are almost √2 rectangles. The A series and the international B series are families that keep the √2 ratio while changing only the size. The JIS B series is a different family based on area, but the finished books have almost the same vertical-to-horizontal ratio.
Japan’s B series is different in size from the international B series. The Japanese JIS B series has an area 1.5 times that of the A series, and B0 is 1.5 square meters. The international B series is different: it falls between the dimensions of adjacent A sizes. So, even for B5, the sizes are different [2]. This difference is a feature of Japanese B sizes.
It is said that the root of Japan’s B sizes is Mino paper, which gained an important position as official stationery for the Tokugawa shogunate during the Edo period [10]. Because there are no clear documents linking the size of Mino paper to B size dimensions, we should only accept this as a "supposed root." The first national standard for book sizes was published in 1929 (Showa 4) as "Finished Dimensions of Paper" [4].
4. Where the Book Size Name "Shiroku-ban" Came From: Large Imported Paper
The name Shiroku-ban does not come from "4 sun by 6 sun." According to an explanation by Mr. Kobayashi, introduced in a paper by Seiko Kitada, the original paper was imported from Britain in the Meiji era for printing. It was close to Crown Fourfold size. This paper was exactly 8 times the size of Mino-ban, so it was called "Dai-hassu-ban" (Large Eight). It was widely used for publishing books and magazines because it was convenient [5].
If you take 32 sheets from this Dai-hassu-ban and finish them, you get a book about 4 sun 2 bu wide and 6 sun 2 bu tall. It is said that booksellers started calling it "Shiroku-ban" from this. The vertical measurement varies by about 1 bu depending on the source, so we do not state it definitively [5]. This paper was also adopted as the format for newspaper rotary press paper after rotary presses arrived after Meiji 20, because the paper was being produced in large quantities at the time [5]. The original sheet dimensions are 788 × 1091 mm for Shiroku-ban and 636 × 939 mm for Kiku-ban [6].
5. How Bunko and Shinsho Books Were Made to Be Easy to Carry
On July 10, 1927 (Showa 2), Iwanami Bunko was launched under Shigeo Iwanami. It is said to have been modeled on the German Reclam Library [8]. Before that, there were other small book series, such as Toyamabo’s "Sleeve Pocket Famous Works Library" in 1903 (Meiji 36). Iwanami Bunko is considered the series that spread and established the "Bunko-bon" format in Japan [11]. The model’s key feature was its small, portable books.
Shinsho books are even more slender. In November 1938, Iwanami Shinsho was launched to help provide "modern learning for modern people." It was the first Shinsho in Japan [9]. The finished dimensions of Shinsho-ban are about 103 × 182 mm [4]. Dividing the height by the width gives about 1.77, which is a more slender shape than the about 1.41 of A and B sizes. We use "about" because the notation varies by source.
A sizes and international B sizes were shapes that used paper efficiently with the √2 ratio. In contrast, Shinsho-ban has a slender vertical shape that is different from that ratio. It is a shape that exists as part of the trend toward small, portable books.
6. Try It Yourself: Measure Three Books and Divide Height by Width
Pick 3 books from your home. Use a ruler to measure the height and width. Use a calculator to divide the height by the width. It is recommended to choose different types, such as Bunko, hardcover books, or magazines. If the result is close to 1.41, the book might be an A or B size. If it is slender like 1.77, it might be a Shinsho size. Measurements have an error of a few millimeters, so compare using "about" numbers. If you want to read more, try opening Lichtenberg’s letter [1] or Seiko Kitada’s paper [5].