Methods of algebraic geometry provide the following parameterization of Fermat's cubic:
In projective space the Fermat cubic is given by
The 27 lines lying on the Fermat cubic are easy to describe explicitly: they are the 9 lines of the form (w : aw : y : by) where a and b are fixed numbers with cube −1, and their 18 conjugates under permutations of coordinates.
- Real points of Fermat cubic surface.
- Ness, Linda (1978), "Curvature on the Fermat cubic", Duke Mathematical Journal, 45 (4): 797–807, ISSN 0012-7094, MR 518106, doi:10.1215/s0012-7094-78-04537-4
- Elkies, Noam. "Complete cubic parameterization of the Fermat cubic surface".
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