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