Fermat cubic

Algebraic cubic surface of equation x^3+y^3+z^3=1

In geometry, the Fermat cubic, named after Pierre de Fermat, is a surface defined by x 3 + y 3 + z 3 = 1. {\displaystyle x^{3}+y^{3}+z^{3}=1.\ } Methods of algebraic geometry provide the following parameterization of Fermat's cubic: x ( s , t ) = 3 t − 1 3 ( s 2 + s t + t 2 ) 2 t ( s 2 + s t + t 2 ) − 3 {\displaystyle x(s,t)={3t-{1 \over 3}(s^{2}+st+t^{2})^{2} \over t(s^{2}+st+t^{2})-3}} y ( s , t ) = 3 s + 3 t + 1 3 ( s 2 + s t + t 2 ) 2 t ( s 2 + s t + t 2 ) − 3 {\displaystyle y(s,t)={3s+3t+{1 \over 3}(s^{2}+st+t^{2})^{2} \over t(s^{2}+st+t^{...