Constant Positive Curvature Surface of Revolution
Constant Positive Curvature Surface of Revolution is a surface of constant positive Gaussian curvature, given by a parametrisation, embedded, with a continuous symmetry group.
Open Constant Positive Curvature Surface of Revolution in the interactive viewer →
aperiodic constant-curvature def-parametric embedded implemented k-const-positive tradition-classical
Properties
- Family
- constant-curvature
- Given by
- a parametrisation
- Curvature
- constant positive Gaussian curvature
- Periodicity
- not periodic
- Ends
- 0
- Embedding
- embedded
- Symmetry kind
- continuous symmetry group
- Fidelity
- exact
Definition
No chart is stored: the spindle/bulge meridian height is an incomplete elliptic integral of the second kind (numerical quadrature in the builder); the one elementary member, a = 1, is the sphere, already charted in charts.py. 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, J. reine angew. Math. 19 (1839) -- the K = +1 classification, mirroring the K = -1 one.