not yet built
Plateau Soap-Film Span
Plateau Soap-Film Span is a physical surface model, of zero mean curvature, given by a parametrisation, immersed.
Open Plateau Soap-Film Span in the interactive viewer →
aperiodic def-parametric immersed implemented minimal physical
Properties
- Family
- physical
- Given by
- a parametrisation
- Curvature
- zero mean curvature
- Periodicity
- not periodic
- Ends
- 0
- Embedding
- immersed
- Fidelity
- exact
Definition
No chart is stored: the soap film spanning a frame is computed by numerical relaxation (minimal_surface_toolkit); nothing closed-form to transcribe. The shipped implementation is authoritative; an unverified transcription would silently define a different surface.
Not yet built
This surface is catalogued but not yet built by the extension, so it has no mesh or thumbnail here.
Sources
Derived from the Math Art generator registries and cross-referenced to the literature; not transcribed from any gallery's compilation.
- Weierstrass-Enneper representation: K. Weierstrass (1866) and
- A. Enneper (1864); the catenoid (surface of Euler, 1744) was shown minimal by J. B. C. Meusnier (1776).
- Costa surface: C. J. Costa (1982); embeddedness by D. Hoffman and
- W. H. Meeks III (1985). Chen-Gackstatter: C. C. Chen and F. Gackstatter (1982). Jorge-Meeks k-noids: L. P. Jorge and
- W. H. Meeks III (1983).
- Triply-periodic families: H. A. Schwarz (P, D; Gesammelte Math.