Half-Twisted Scherk Surface
Half-Twisted Scherk Surface is a singly periodic minimal surface, given by a Weierstrass representation, immersed, with a rod group.
Open Half-Twisted Scherk Surface in the interactive viewer →
def-weierstrass immersed implemented minimal minimal-periodic singly-periodic tradition-classical
Properties
- Family
- minimal-periodic
- Given by
- a Weierstrass representation
- Curvature
- zero mean curvature
- Periodicity
- singly periodic
- Ends
- 0
- Embedding
- immersed
- Symmetry kind
- rod group
- Fidelity
- exact
- Exactness
- numerical-integral
Definition
Weber's singly periodic surface with two annular and two helicoidal ends -- the simpler surface with the same end types as Scherk's fourth surface, which the Scherk IV post says he found accidentally.
Sources
Derived from the Math Art generator registries and cross-referenced to the literature; not transcribed from any gallery's compilation.
- H. F. Scherk, "Bemerkungen ueber die kleinste Flaeche innerhalb gegebener Grenzen", J. reine angew. Math. 13 (1835) 185-208 -- the fourth surface of that paper.
- M. Weber, "The half-twisted Scherk surface", "Scherk's fourth surface", "Plane with catenoids", minimalsurfaces.blog (Indiana University) -- the closed-form Weierstrass pairs transcribed here.
- H. Karcher, "Construction of minimal surfaces", Surveys in Geometry, Univ. of Tokyo (1989), and Lecture Notes No. 12, SFB 256, Bonn (1989)
- - the half-catenoid chain and field.
- The 3DXM Consortium, "Chain of Half-Catenoids and Field of Half-Catenoids", Virtual Math Museum, virtualmathmuseum.org.
- M. Weber, 'The Half-Twisted Scherk Surface', minimalsurfaces.blog (local mirror: minsurf/book/.../ch152_the_half_twisted_scherk_surface.md).