Paperfolding

It is a curious fact that until 2002, mathematicians thought that the maximum number of times you could fold a single sheet of paper in half was seven times. In 2002, a junior high student named Britney Gallivan proved them wrong, demonstrating a way to fold a 1200m length of toilet paper in half 12 times. It’s a heckuva way to get famous, but it seems to have worked out for her.

We are, thankfully, not going to fold anything more than four times, but it’s nice to know it’s an option.

Let’s get some terminology out of the way.

By now, you know I’m not a huge stickler for trade-specific nomenclature. A knife by any other name will cut off your finger just the same.

Books, however, are defined by how many leaves result from a folded page once sewn and cut. Folded once, it was folio (four pages on two leaves); twice, it became quarto (eight pages on four leaves); thrice, octavo (16 pages on 8 leaves); four times, sextidecimo (32 pages on 16 leaves).

FOLIO QUARTO OCTAVO ETCETERA

While there could, theoretically, be smaller sizes, we won’t go past sextidecimo, if even that.

Each bundle of folded paper, once it has been cut into individual leaves, forms a signature. Signatures are sewn together to form the text block or book block. (In later periods, books were sometimes left with one edge uncut and the buyer could slice them open on first reading. I have some 19th century tomes with uncut signatures in my collection.)

An Imposition

“In 1548, Francois I decreed standard paper sizes for France and arrested all who disobeyed. To cut waste and use every bit of paper surface, printers devised ‘the imposition’ — complicated sets of topsy-turvy pages printed in two passes on a large press sheet . . . folded, trimmed, and sewn, all the pages appear right side up and in proper sequence.”
Michael Olmert, Smithsonian Book of Books, pg 164, (sidebar)

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If you fold a piece of paper four times as I have done above, then number each face of the fold in order (I used Post-it notes because reaching inside the folds with a pencil was annoying) when you unfold the paper and lay it flat once more, you’re going to have something that looks like this.

(Imagine each set of eight rectangles is the front or back of the sheet of paper.)

A plain sheet of paper, divided in eight rectangles to indicate the folded leaves. Numbered, from the upper left: 14, 3, 2, 15 and then the bottom row, upside down: 11, 6, 7, 10.
front
A plain sheet of paper, divided in eight rectangles to indicate the folded leaves. Numbered, from the upper left: 16, 1, 4, 13 and then the bottom row, upside down: 9, 8, 5, 12.
back

Fold a piece of paper in half four times and try it yourself.

This layout technique (somewhat more refined) works in any case for any size book. A printer, laying out the leaded type and engravings for a text can use this trick to orient the pages correctly so that they form a coherent narrative, each page falling into place as the pages are folded and cut, forming a book with page one at the front and page (whatever) at the back and all the numbers between falling in proper sequence.

Being able to print 16-32 pages at a time is an enormous boost to production over printing each page individually and assembling them later.

Print, dry, fold, cut, sew, cover, boom! Book.

More papercuts later.

~ Scott


Fun book nerd trivia: Do you see now why almost every printed book you’ve ever read had a bunch of blank pages at the back of the book? To this day, printing presses use some version of this same layout technique (seriously, grab any hardback near at hand and check) and even eBooks are usually formatted with an even number of pages to perpetuate the results of physical press imposition.

Works referenced

Britney Gallivan, Wikipedia article

Scrunch Time: The peculiar physics of crumpled paper, New Scientist (magazine), December 20, 2011, accessed November 8, 2018

The Smithsonian Book of Books by Michael Olmert, Smithsonian Books, Washington D.C., 1992

The Complete Book of Papermaking, Josep Asunción, Lark Books 2003

Additional reading:

Adventures in Pouncing — Our own earlier post on papermaking in England is mostly about additives used to make paper work with ink, but covers the nature of papermaking in England in some detail.

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