
The optimal way of folding a bond notebook page into a bookmark - zhamisen
https://arxiv.org/abs/2002.02622
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divbzero
I love how:

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

2\. HN comments do the same.

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throwawy200210
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"?

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kwhitefoot
Bond is fine writing paper.

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kwhitefoot
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.

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aesthesia
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.

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skykooler
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.

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CliffStoll
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.

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whitten
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 ?

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

This:

[https://en.wikipedia.org/wiki/Doubling_the_cube](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.

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ttugrq
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.

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sonofaplum
very very carefully

