The optimal way of folding a bond notebook page into a bookmark | Hacker News Reader

The optimal way of folding a bond notebook page into a bookmark

arxiv.org

46 pointszhamisen13 comments

I love how:

1. The author treats this topic so seriously and thoroughly.

2. HN comments do the same.

Can anyone explain what the author means by "bond" in this context? Is it a specific mathematical term, or did they mean to write "bound"?

The author is confusing bond with bound. The introduction contains this sentence: "Second, all pages are bond from the top and cannot be torn off."

Bond is fine writing paper.

Ah, silly me, I should have read the article and not just the comments. Bond does indeed describe the paper but as someone else pointed out it isn't what the article is talking about.

I think there's an error here in the case of a very tall notebook. The paper claims that there is a finite limit to how far to the right the bookmark can go. But it seems to me that for a sufficiently tall sheet of paper, the optimal fold is at a 45 degree angle with the left edge of the paper folded right up to the top edge. This gives you a length of D - 1 hanging to the right, where the width of the paper is 1 and the height is D.

I believe "tall" here refers to the length of the spine of the notebook, in which nomenclature what you're referring to is a "wide" paper.

Isn’t this the special case covered near the top of page 8?

The Huzita-Hatori axioms are at the core of thin-sheet origami. In turn, mathematical origami is hot stuff, not only because of its applications (folding automotive airbags, designing mirror & solar panel assemblies for spacecraft) but also because it's opening up novel areas of mathematical research.

quoting from the paper: Although innocent at the first glance, origami surpasses the power of “compass and straight-edge”and can solve third-order mathematical problems including the “angle trisection” and “doubling the cube”

quoting from the paper: From the technological side, origami is a generic methodology to transform between 2d and 3dgeometries.

Does anyone know if you had a mechanical "liquid paper notebook" where the marks on the notebook are rotating micro-balls (from 0% to 100% black) if you could use origami as a way of expanding out an originally folded sheet of a large size (say 11 x 14 - legal size paper) where the folded version might be the size of a paperback book?

On a different note, I think I know what angle trisection is, but I'm not sure what "doubling the cube" might mean.

Does anyone know what geometric problem the author is referencing ?

> I'm not sure what "doubling the cube" might mean.

This:

https://en.wikipedia.org/wiki/Doubling_the_cube

It's basically being able to construct the cube root of two; you can't construct roots that aren't powers of two with a compass and straightedge.

An engineers approach: grab one corner and gently pull it to where it seems like a maximum, then smoosh the book closed. You immediately find that two folds get much farther than one.

very very carefully

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