https://www.homedepot.com/p/Milwaukee-100-ft-Bold-Line-Chalk...
One can create an axiomatic system of geometry through such coincident folds (as an alternative to straight-edge and compass) and it turns out to be more powerful than the Euclidean system.
One can construct cube roots, trisect angles.
Depending on the choice of paper folding axioms one can go beyond cube roots and k-secting angles to the entire set of algebraic numbers.
thank you!
My best (worst) HN days are like that :)
I don't think that's sufficient--tinfoil doesn't stretch, but it doesn't fold nearly as neatly as paper.
Most metals are stretchier than paper. If it is thick it will resist folding, but once you have folded it, that is, the two flat boundary surfaces have coincided, the crease would be a straight line if the surfaces cannot stretch.
How much force you will need to exert to form a fold depends on material properties but the geometrical nature of the crease is dictated by stretching.
https://news.ycombinator.com/item?id=48538771
by roelschroeven.
I often wondered how to ensure that the corners of a sheet of paper make a right angle. You need that to form a square sheet, otherwise the standard trick of folding along the diagonal gives a rhombus, not a square.
A sheet of paper approximates a Cartesian plane probably more closely than most things we can fold
Therefore a fold will always be in line with the theoretical 2D plane and thus will be the shortest (straight) line.
A string made taut between two points is surely a better way? And works at much bigger sizes too (people build walls and foundations using this technique all the time). The paper is less useful in practice because any paper you find is probably straight and square anyway.
Still, I had fun thinking about this as I definitely hadn't considered it before.
BTW, your method was the method of choice for the surveyors of the Nile, from the Egyptian civilization.
Paper is hi-tech and was not available until much later, and as you mentioned doesn't scale. But if I have misplaced my ruler ...