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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