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.
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.
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 ?
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.
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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[ 3.6 ms ] story [ 45.1 ms ] threadquoting 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 ?
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.
1. The author treats this topic so seriously and thoroughly.
2. HN comments do the same.