# Nicomedes's Geometric Construction of Principal Cube Root

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 .

△ABC

k/4

AB=k/4

0<k<4

M

AB

B

CD

E

C

AB

S

BA

R

DE

SC

RS=1

AS=

3

k