The optimal way of folding a bond notebook page into a bookmark(arxiv.org)
arxiv.org
The optimal way of folding a bond notebook page into a bookmark
https://arxiv.org/abs/2002.02622
13 comments
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.
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 ?
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.
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
1. The author treats this topic so seriously and thoroughly.
2. HN comments do the same.