Fermat Space is the solution set of the equation z1^n + z2^n = 1, for complex numbers z1, z2 and integer n, plotted here for n=3. It is projected from the 4-dimensional complex projective space CP^2 into 3 dimensions to create the model. (This space is an extension of Fermat's famous "last theorem", which was that this equation has no real rational solutions for n>2.) The graphics were developed by Andrew J. Hanson of Indiana University, plotted in Mathematica, and thickened in Blender.
Fermat Space is closely related to the 6-dimensional Calabi-Yau space, which represents the 6 'hidden' dimensions of 10-dimensional string theory. The C-Y space is the solution set of the Fermat Space with n=5.
C-Y space is the solution set of a degree five polynomial (n=5) with complex variables.
4.552 w x
4.45 d x
1.792 w x
1.752 d x