Henneberg (one-sided)
Henneberg (one-sided) is a minimal surface, given by a Weierstrass representation, immersed.
Open Henneberg (one-sided) in the interactive viewer →
aperiodic def-weierstrass immersed implemented minimal non-orientable tradition-classical
Formula
Properties
- Family
- minimal
- Given by
- a Weierstrass representation
- Curvature
- zero mean curvature
- Periodicity
- not periodic
- Ends
- 0
- Embedding
- immersed
- Orientable
- no
- Fidelity
- exact
- Exactness
- numerical-integral
Definition
Extracted from the shipped row's source by AST (complete multi-line lambdas, g/dh lambdas) and reproduced numerically against the shipped callables over the complex plane, exactly -- no scalar slack.
Sources
Weierstrass data reproduced numerically against the shipped implementation (math_art/minsurf/zoo.py, row HENNEBERG_RP2) by sampling g and dh over rings in the complex plane at the row's default parameters: g: matches over 144 complex samples (worst 0); dh: matches over 144 complex samples (worst 7.59e-15).
- L. Henneberg (1875); R. Kusner, Bull. Amer. Math. Soc. 17 (1987) 291-295; F. J. Lopez, Duke Math. J. 71 (1993) 23-30 -- full citations in the weierstrass symtail engine block.
- B. Riemann (1867) and F. J. Lopez, A. Ros, J. Differential Geom. 33 (1991) for the (never embedded) finite Riemann family; the symmetrized member follows M. Weber, minimalsurfaces.blog, "Symmetrized Finite Riemann".
- H. Karcher, "Construction of minimal surfaces" (1989) for the symmetrization method (double Enneper, k-noid families);
- L. P. Jorge, W. H. Meeks III, Topology 22 (1983) for the k-noids; data after M. Weber, minimalsurfaces.blog ("Symmetrized Double Enneper", "k-Noids with Enneper Ends", "Antiprismatic k-Noids").