Fermat cubic

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In geometry, the Fermat cubic, named after Pierre de Fermat, is a surface defined by

x^3 + y^3 + z^3 = 1. \

Methods of algebraic geometry provide the following parametrization of Fermat's cubic:

x(s,t) = {3 t - {1\over 3} (s^2 + s t + t^2)^2 \over t (s^2 + s t + t^2) - 3}
y(s,t) = {3 s + 3 t + {1\over 3} (s^2 + s t + t^2)^2 \over t (s^2 + s t + t^2) - 3}
z(s,t) = {-3 - (s^2 + s t + t^2) (s + t) \over t (s^2 + s t + t^2) - 3}.

Image:FermatCubicSurface.PNG

Fermat cubic surface.


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