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The problem of trisecting the angle is a classic problem of compass and straightedge constructions of ancient Greek mathematics.
Problem: construct an angle onethird a given arbitrary angle, given only two tools:
With such tools, it is generally impossible, as shown by Pierre Wantzel (1837). This requires taking a cube root, impossible with the given tools. The fact that there is no way to trisect an angle in general with just a compass and a straightedge does not mean that it is impossible to trisect all angles so.
Contents
Perspective and relationship to other problems
Using only an unmarked straightedge and a compass, Greek mathematicians found means to divide a line into an arbitrary set of equal segments, to draw parallel lines, to bisect angles, to construct many polygons, and to construct squares of equal or twice the area of a given polygon.
Three problems proved elusive, specifically:
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