Drawing a 3D representation of complex Fermat curve x^n + y^n = 1

*To*: mathgroup at smc.vnet.net*Subject*: [mg74773] Drawing a 3D representation of complex Fermat curve x^n + y^n = 1*From*: "Ben" <benlotto at gmail.com>*Date*: Wed, 4 Apr 2007 04:11:49 -0400 (EDT)

On page 233 of my edition of Simon Singh's book Fermat's Enigma, there is a figure (Figure 20) of two surfaces. The caption says that they are "geometrical representations of equation x^n + y^n = 1, where n=3 for the first image and n=5 for the second. here, x and y are regarded as complex variables." My question is what projection was used to represent a complex surface in complex 2-space as a surface in real 3-dimensional space. If anyone knows some Mathematica code that generated these images, I'd love to see it. Many thanks, -Ben Lotto