Math Art
Finite Riemann (plane + 2 catenoids)

Finite Riemann (plane + 2 catenoids)

Finite Riemann (plane + 2 catenoids) is a minimal surface, given by a Weierstrass representation, immersed.

Open Finite Riemann (plane + 2 catenoids) in the interactive viewer →

aperiodic def-weierstrass immersed implemented minimal tradition-classical

Formula

Gauss map g
t⁢(3+z2)−1+z2\frac{t \left(3 + z^{2}\right)}{-1 + z^{2}}
Height differential dh
3+z2−1+z2\frac{3 + z^{2}}{-1 + z^{2}}

Properties

Family
minimal
Given by
a Weierstrass representation
Curvature
zero mean curvature
Periodicity
not periodic
Ends
0
Embedding
immersed
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 M3_FRIEM) 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 0).