Amsler Surface
Amsler Surface is a surface of constant negative Gaussian curvature, given by a parametrisation, self-intersecting.
Open Amsler Surface in the interactive viewer →
aperiodic constant-curvature def-parametric implemented k-const-negative self-intersecting tradition-classical
Properties
- Family
- constant-curvature
- Given by
- a parametrisation
- Curvature
- constant negative Gaussian curvature
- Periodicity
- not periodic
- Ends
- 0
- Embedding
- self-intersecting
- Fidelity
- exact
Definition
No chart is stored: defined through a Painleve III ODE that the builder integrates with RK4; no closed form exists. The shipped implementation is authoritative; an unverified transcription would silently define a different surface.
Sources
Derived from the Math Art generator registries and cross-referenced to the literature; not transcribed from any gallery's compilation.
- M.-H. Amsler, 'Des surfaces a courbure negative constante dans l'espace a trois dimensions et de leurs singularites', Math. Ann. 130 (1955).