Enneper's Negative Curvature Surfaces

The Enneper surfaces are a three-parameter family of surfaces with constant negative curvature (and nonconstant MeanCurvature). In general, they are described by Elliptic Functions. However, special cases which can be specifiedparametrically using Elementary Functions include the Kuen Surface, Rembs'Surfaces, and Sievert's Surface.

References

Enneper, A. ``Analytisch-geometrische Untersuchungen.'' Nachr. Königl. Gesell. Wissensch. Georg-Augustus-Univ. Göttingen 12, 258-277, 1868.

Fischer, G. (Ed.). Plate 92 in Mathematische Modelle/Mathematical Models, Bildband/Photograph Volume. Braunschweig, Germany: Vieweg, p. 88, 1986.

Reckziegel, H. ``Enneper's Surfaces.'' §3.4.4 in Mathematical Models from the Collections of Universities and Museums (Ed. G. Fischer). Braunschweig, Germany: Vieweg, pp. 37-39, 1986.

• Relative Minimum
• Relaxation Methods
• Remainder
• Remainder Theorem
• Rembs' Surfaces
• Removable Crossing
• Removable Singularity
• Rencontres Number
• Rendezvous Values
• Repartition
• Repdigit
• Repeating Decimal
• Repfigit Number
• Replicate
• Representation
• Reptend Prime
• Rep-Tile
• Repunit
• Residual
• Residual vs. Predictor Plot
• Residue Class
• Residue (Complex Analysis)
• Residue (Congruence)
• Residue Index
• Residue Theorem (Complex Analysis)