Crochet Hyperbolic Surface
Crochet Hyperbolic Surface is a surface of constant negative Gaussian curvature, given by a parametrisation, immersed.
Open Crochet Hyperbolic Surface in the interactive viewer →
aperiodic constant-curvature def-parametric immersed implemented k-const-negative
Properties
- Family
- constant-curvature
- Given by
- a parametrisation
- Curvature
- constant negative Gaussian curvature
- Periodicity
- not periodic
- Ends
- 0
- Embedding
- immersed
- Fidelity
- exact
Definition
No chart is stored: grown by a discrete stitch-increase rule, row by row; the surface is the crochet fabric itself, not a formula. 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.
- Daina Taimina, "Crocheting Adventures with Hyperbolic Planes", A K Peters, 2009; David W. Henderson and Daina Taimina, "Crocheting the hyperbolic plane", Math. Intelligencer 23(2), 2001, pp. 17-28.
- Self-similar buckling / distributed branch points of constant- negative-curvature elastic sheets: John A. Gemmer, E. Sharon,
- S. C. Venkataramani et al., "Distributed branch points and the shape of elastic surfaces with constant negative curvature", arXiv:2006.14461.
- Hilbert's theorem (no complete C^2 isometric immersion of H^2 in R^3): D. Hilbert, Trans. AMS 2, 1901, pp. 87-99.