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In differential geometry and algebraic geometry, the Enneper surface is a self-intersecting surface that can be described parametrically by:
The Weierstrass–Enneper parameterization is very simple, f = 1 , g = z {\displaystyle f=1,g=z} , and the real parametric form can easily be calculated from it. The surface is conjugate to itself.
Implicitization methods of algebraic geometry can be used to find out that the points in the Enneper surface given above satisfy the degree-9 polynomial equation
Dually, the tangent plane at the point with given parameters is a + b x + c y + d z = 0 , {\displaystyle a+bx+cy+dz=0,\ } where
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