This may seem like a dumb question. Likely there is a simple answer that I haven’t considered.
The earliest architects and engineers must have needed a straight edge to draw lines for accurate calculations. Nothing, at least that I know of, in nature is a precise physical straight line. I suppose a thin piece of metal could be bent for a straight edge, but this would require that the metal be hammered into a perfectly flat plane. A stretched length of string would be roughly a straight edge, but not a great way to draw a straight line. (As it would bend with the pressure of a writing utensil.)
I would wager that the answer lies in the fact that the surface of liquid forms a flat plane. But how that was transfered to a straight edge is beyond my limited cleverness.
Take the string and impregnate it with ink, graphite, or even charcoal. Stretch it and pluck it, i.e., lift it perpendicular to the surface then release. Voila!
Those techniques work just fine if I have modern saws, files, sandpaper, and advanced measuring tools. It’s interesting in that I’ve not really considered that people need to make their own reference edges these days.
I’m not sure it is applicable to ancient methods. It also seems like fairly advanced thinking and technique.
Maybe another interesting question would be “when was the first straight edge needed and used for architectural, engineering and/or mathematic purposes?
I suppose that might be straight enough, although there are inconsistancies in the material of the string that would make it less than a perfect straight line.
At some point in time, though, an actual straight edge was made. How?
Letting a sheet of some form of fine clay/water mixture to cure might give it a flat enough surface due to gravity. Then maybe some how cut that into a strip to give you a straight edge to pass a pencil across.
From there, you would gradually build and refine more accurate edges, until you could create a nice ruler or square out of wood, or metal.
I’ll bet we’re missing a very simple solution though, that our modern minds are blind to.
I’d say all you have to do is fold something. You give me the most irregular piece of cardboard, tin, etc., all I have to do is fold it over once flat and voila—a straight edge.
Well, if you want perfection, there aren’t any even today; just sucessively better refinements. I suspect the real answer to your question is that they found something close enough. Sighting along an edge will tell you if it’s straight to a very high degree, and if it isn’t, you sand/scrape/whatever. The current theory is that the parthenon stones were flattened by simply putting another stone slab on top of them and moving them in a circle on each other for a long time – wearing them down to two flat surfaces. The stone fittings of the pyramids were likely created the same way, although it’s harder to prove.
And the bit about no straight lines in nature always bugged me; you get into a “No True Scotsman” thing about what a straight line is pretty quick, but there are LOTS of straight lines in nature: the edge of a half-moon, the strands of spider webs, the shape described by anything hanging on a calm day, the path described by any falling object from at least one angle, the surface of water, crystal edges, shear patterns in stone/mud/moved earth, beams of light, the edge of anything folded or bent, scratches of a hard object thrown against another, sight and shadow lines, breakage patterns in stone, and on and on. Even the surface of the ocean is likely straighter than the ruler you used in school, curvature of the earth notwithstanding.
If you want something as straight as a rule, all you have to do is get it approximately straight, use it to draw a fine line, then flip it over and draw another line immediately touching the first - if it’s not straight, the deviations will show you where to remove material from the edge.
It’s been a while since I saw bricklayers at work, but one tool that they used to use to get bricks in a straight line was string. I think that would have been available to the Egyptians and the Greeks as they built the pyramids and the Parthenon.
You can also use a piece of string to construct a right angle for the corners of your pyramid, temple, etc.: mark off 12 equal sections on the string, then (with a couple of friends if the string is long enough) make a 3-4-5 triangle. As Pythagoras knew (but did not discover) the largest angle of that triangle is a right angle.
It’s a damned good line for construction purposes. This is the purpose of a chalk line – a string on a spool in a housing filled with chalk. You have one guy hold the end while the other guy walks out the line. They hold it taut a couple of inches above the surface and snap it as indicated. You get a very staight line for building or painting. I’ve done it myself often enough.
As for a straight surface – liquids allowed to sit still will produce a very good flat surface. If you let something that is liquid congeal or solidify, it will have a very straight surface you can use as a reference.
This is a mantra I often recite to myself. The people of thousands of years ago were just as intelligent as we are today. They had less technology, less absolute knowledge, and less history to learn from, but their reasoning ability was just as sharp. If they could find ways to apply the things they learn and discover, they could achieve no end of amazing things. And, indeed, they did.
FYI the earliest known devices to draw theoretically straight lines are the Sarrus linkage and the Peaucellier-Lipkin linkage.
The arms of the Peaucellier-Lipkin linkage don’t have to be straight. Only the indicated distances must be equal. This can be accomplished by stacking those arms and drilling through them all at once.
I’m not sure if an analogous construction method can be used with the Sarrus linkage, but it seems simple enough that the ancients could have discovered it.
In optics, you grind surfaces by rubbing them together with some kind of abrasive. The surfaces become spherical while you do this, with the radius depending on the strokes you use. Spherical surfaces are the only ones that remain in contact throughout all the sliding and rotating.
A special case is the flat surface, which you could always consider spherical with infinite radius. Opticians can make very flat surfaces by grinding together three different objects, two at a time, and changing out which of the three is set aside. Flat surfaces are the only surfaces such that 3 of them will mate this way.
Not necessarily. If you do that with an S-shaped edge (or any edge that is rotationally symmetric about its middle), there will be no deviation between the edge and the line. I think you need three edges, like ManiacMan’s link and Napier said.
I said flip - you’re rotating (OK… we’re both rotating - but what I mean is draw a line against the would-be-straight edge, then flip the piece over the line you just drew.