Nicomedes's Geometric Construction of Principal Cube Root
This Demonstration shows Nicomedes's method for constructing a cube root using a marked ruler. (Nicomedes was born about 270 BC.) This is actually the real principal cube root. Every nonzero number also has a pair of complex conjugate cube roots.
Let have sides of length , 1 and 1, where with . Let be the midpoint of and let be the midpoint of . Let be a point on the line through parallel to . Let be a point on the ray and be the intersection of segments and . If , then .