Meeks Mobius Strip

Meeks Mobius Strip is a minimal surface, given by a Weierstrass representation, immersed.

Open Meeks Mobius Strip in the interactive viewer →

aperiodic def-weierstrass immersed implemented minimal non-orientable tradition-classical

Formula

Gauss map g

\frac{z^{2} \left(1 + z\right)}{-1 + z}

Height differential dh

i - \frac{i}{z^{2}}

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, phi triple (dh = phi3, g = phi3/(phi1 - i*phi2), a Weierstrass-representation identity)) 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 MEEKS_MOBIUS) by sampling g and dh over rings in the complex plane at the row's default parameters: g: matches over 144 complex samples (worst 1.06e-12); dh: matches over 144 complex samples (worst 9.93e-16).

R. Schoen / Lopez & Ros (1991) on the Lopez-Ros deformation; H. F. Scherk (1835) for the base Scherk surface; the decorated-Enneper symmetrization follows M. Weber's repository, https://minimalsurfaces.blog/ (Enneper with n Catenoids).