Cool, a maths "Construction" means a geometric arrangement, it's different from material craft and construction.

@a_donda: Not compass, as in magnetic compass, but compass as in used to draw a circle or measuring multiples of a known distance (often also in the latter case called dividers.

How is this not answered by a simple Google search, where numerous videos on making a straight edge with hand tools such as saw and plane are found, as here.

@Pieter Geerkens, This is not answered by google search, because it gives: en.wikipedia.org/wiki/Straightedge_and_compass_construction ... because the oldest known planes date from after the Greeks, They solved quadratic equations using geometry and needed a perfectly straight edge. The straight edge would be less straight than the base of the plane, which may be concave or convex.

What clarification, and what take back. The question clearly states: "Greeks used a compass and a straightedge for geometry." Magnetic compasses for navigation are of no value what so ever for geometry.

@com.prehensible: Don't be absurd. The entire point of bootstrapped tool manufacturing is to make the tool of each generation more precise than it's equivalent in the previous generation. if that were not possible, it would have been impossible to ever make a better tool. While the first wood planes similar to the modern design were likely built by the Romans, that ancient Egyptians created mortice and tenon joints requires that they were very familiar with how to plane wood using more primitive tools.

In english speaking countries, it is customary to not say "don't be absurd" unless you want to say "you are being idiotic"... it's kind of like "suck it" level of etiquette in scientific discourse. just a point of note. It's both a command and an insult. Of course we all know about bootstrapped tool manufacture, especially programmers.

Actually this question was provoked by a discussion in the mathematics forum stating it would have been impossible to make a precisely straight edge... so i am not the only one with this absurd logic, it comes from maths. stack.

@com.prehensible: Being smart is no measure of either common sense or knowledge.

Wood is not a very precise material. It changes with humidity and has other imperfections. They may have made a metal straight edge, which can't be planed. There was no reason to presume that pythagoras etc favored the use a wooden straight edge. If you dry wet gypsum mixed with sand, you can obtain a very straight plane for sanding, which can be used to make a metal straight edge. And I didn't find any information for boostrapping straightness, it works fine these days because of calipers which use screws for fine adjustment.

A geometric method to produce a straightedge is described in the book by M. Berger, Geometry revealed (Springer 2010) on p. 116. Greek mathematics had no tools to justify this method, but it is possible that they knew it empirically.