There is some real math behind the rectangular sheets of paper. At least if you work with ISO paper sizes. Measurements of the widespread A4 are derived from the size of A0 – it has an area of exactly 1 m2. For the B series every next size is also half as large (or twice as large – depending on the direction you choose to go) as the previous. B0 is defined by the length of its larger side – it is exactly 1 meter long. Both of them have the same aspect ratio: square root of 2.
But what if you want to sew your book with sheets of paper of a non-standard form and aspect ratio? There are some issues to consider. And not only during the bookbinding process, but also for the future use of the book. For example, most of the bookshelves are designed to store only rectangular books. The other issue is the form of the sheet itself. It will take more time for a bookbinder to prepare non-standard sheets. There would also be more waste after the work is done.
I can remember one nice and beautiful example of the use of non-standard paper in fiction: Battlestar Galactica characters had sheets of paper (printed documents, photographs, etc.) of rectangular form with all the four corners cut. It has also affected the books they’ve used: books corners were cut at the right edge leaving the spine intact.
Here is something even stranger: pie books. From time to time, I see photos of these triangular books in my Facebook feed. I’m not I want to try creating one, but they definitely attract my attention. To make a pie book you need to prepare sheets of paper in a form of a rhombus. You fold them in half and get signatures with triangular pages (don’t forget about the grain direction!)
Here is an origami tutorial on making a triangular piece of paper out of the standard rectangular sheet. You just need to use a folded sheet of paper to get a rhombus instead of a triangle.
Then you just procced with sewing as usual, to get something like these:
More pie books I have found at the Marina Books Etsy store:
Pie books by the Boundless Bookbindery. Here you have a chance to look inside!
As a bonus, paper sizes explained: