> In fact I don't know of any other good way of obtaining a straight edge from scratch quickly
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.
Over long distances the string will sag in the middle. That's one of the reasons (not the only reason) construction uses lasers today.
yeah its pretty hard to get new help to pull hard without fear of breaking the tool, coincidentally the beam width of a laser will increase over long distance, similar to line slack sagging over long distance.
The DeWalt that I've been using recently had a bright green line pencil thin, in the sun, easily ten meters from the device. That's far enough to do an entire patio - ten meters in each direction. I don't know about longer needs, such as sidewalks, but for building construction the DeWalt was excellent.
I've never tried other brands.
the really serious guys use GPS based equipment, and its serious stuff, being able to center up on a 1/64 inch brad tacked into the asphalt.
[that 50,000$ ufo on a tripod by the highway, dont try to steal one, man do they ever know exactly where they are]
yeah i like team yellow too :) the beam spread is what you want to check out if your serious about > 100 ft distance
https://www.gpsalaska.com/
^ this is a very commercial website, but example of higher end equipment and technique
How do you calibrate the GPS
there is a sattelite network, and a terrestrial reference station infra
Yeah but how do we know there distances accurately
usually laser ranging is used to establish a baseline, rather than using a theodolite and chain like OG surveyors.
the rest is trigonometry, withe the GPSS defining points relative to the baseline.
https://www.gps.gov/trilateration
https://apps.dtic.mil/sti/html/tr/ADA165932/index.html
https://app.studyraid.com/en/read/15241/528230/determining-d...
It depends what you need that line for -- if you're projecting onto a wall, that sag matters. If you're projecting onto the ground, it doesn't.
Folded paper won't?
If anybody has ever tried folding a very large paper (or, bedsheets, tarps, etc), they'll realize the wisdom of this comment. Our intuition from folding paper on the order of several to tens of centimetres does not scale to arbitrary size and precision. Paper is relatively rigid, but its rigidity is finite and ensuring local-to-global flatness becomes a painstaking endeavour.
Then there is the puzzle of coming up with folds to intentionally increase the rigidity of the surface. Essentially, using Theorema Pizzarium
Folded paper has some structure, so not as much?
I have an asterisk in my post addressing that :) Happy to have picqued your mind.
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 ...