How to divide a piece of paper into an odd number of sections?

In yesterday’s edition of Monica Langwe’s bookbinding-focused email newsletter she mentioned the book The Art of the Fold:

I am glad to hold “The Art of The Fold” in my hands. The book, made together with her daughter Ulla Warhol, is tastefully created and a “must have” for all working with bookbinding in a creative way.

Thank you Hedi for sharing your knowledge. I always talk about  you in my courses and I am truly happy for having had the opportunity to work with you!

Per my new habit for finding good books, I checked the website for The Bookmark and found, to my surprise and delight, that they had a copy in stock. And that they closed in 20 minutes.

So I hoofed over to the store and bought it (sorry–it was the last one; more are on order).

There is a Techniques section early in the book, and the section “Dividing into an odd number of sections” caught my eye:

This is something I’ve struggled with a lot in my bookbinding experiments, as when stitching a binding it’s very common to need an odd number of sections along the spine of the book.

But I found the explanation, especially the visual, in The Art of the Fold confusing because it shows a piece of paper that happens to neatly fit along the hypotenuse of a 5x5 triangle, and that’s often not the case.

What I realized is that it’s best to ignore the illustration, and follow the theory; here’s my experiment:

The key to figuring this out for me was that the X axis can be ignored completely; it’s only the Y axis that matters.

So the bottom-left corner goes at 0,0, and the top-right corner is set to wherever it lands on the Y axis at the number of sections you want (in this case 5). Then the Y axis markings–1, 2, 3, 4– are used to mark the sheet into that number of sections.

My confusion or not, it’s a great hack, and worth the price of the book already.

I’m very excited about being able to dive deeper into The Art of the Fold.