Minding Surface
Minding Surface is a surface of constant negative Gaussian curvature, given by a parametrisation, embedded, with a continuous symmetry group.
Open Minding Surface in the interactive viewer →
aperiodic constant-curvature def-parametric embedded implemented k-const-negative tradition-classical
Properties
- Family
- constant-curvature
- Given by
- a parametrisation
- Curvature
- constant negative Gaussian curvature
- Periodicity
- not periodic
- Ends
- 0
- Embedding
- embedded
- Symmetry kind
- continuous symmetry group
- Fidelity
- exact
Definition
No chart is stored: the meridian height z = integral sqrt(1 - a^2 sinh^2 t) dt is an incomplete elliptic integral, integrated numerically (Simpson) by the builder. 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.
- F. Minding, 'Wie sich entscheiden lasst, ob zwei gegebene krumme Flachen auf einander abwickelbar sind oder nicht', J. reine angew. Math. 19 (1839).