Zoll's Surface
Zoll's Surface is a surface of revolution, given by a parametrisation, genus 0, embedded.
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aperiodic closed closed-orientable def-parametric embedded implemented revolution tradition-classical
Properties
- Family
- revolution
- Given by
- a parametrisation
- Curvature
- no condition imposed
- Periodicity
- not periodic
- Genus
- 0
- Ends
- 0
- Embedding
- embedded
- Orientable
- yes
- Fidelity
- exact
Definition
No chart is stored: the height z(u) is a per-point Gauss-Legendre quadrature of a non-elementary integral (the Tannery variants of the same builder ARE closed-form and are charted). 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.
- O. Zoll, 'Uber Flachen mit Scharen geschlossener geodatischer Linien', Math. Ann. 57 (1903).
- J. Tannery (1892) for the earlier, non-smooth example.