Math Art
Sievert's Surface

Sievert's Surface

Sievert's Surface is a surface of constant positive Gaussian curvature, given by a parametrisation, self-intersecting.

Open Sievert's Surface in the interactive viewer →

aperiodic constant-curvature def-parametric implemented k-const-positive self-intersecting tradition-classical tradition-physical-model

Formula

x(u, v)
2⁢2+2⁢sin⁡(u)2⁢sin⁡(v)2−sin⁡(v)2⁢cos⁡(u)2⁢cos⁡(−u2+atan⁡(2⁢tan⁡(u)))\frac{2 \sqrt{2 + 2 \sin\left(u\right)^{2}} \sin\left(v\right)}{2 - \sin\left(v\right)^{2} \cos\left(u\right)^{2}} \cos\left(\frac{-u}{\sqrt{2}} + \atan\left(\sqrt{2} \tan\left(u\right)\right)\right)
y(u, v)
2⁢2+2⁢sin⁡(u)2⁢sin⁡(v)2−sin⁡(v)2⁢cos⁡(u)2⁢sin⁡(−u2+atan⁡(2⁢tan⁡(u)))\frac{2 \sqrt{2 + 2 \sin\left(u\right)^{2}} \sin\left(v\right)}{2 - \sin\left(v\right)^{2} \cos\left(u\right)^{2}} \sin\left(\frac{-u}{\sqrt{2}} + \atan\left(\sqrt{2} \tan\left(u\right)\right)\right)
z(u, v)
log⁡(tan⁡(v2))+4⁢cos⁡(v)2−sin⁡(v)2⁢cos⁡(u)2\log\left(\tan\left(\frac{v}{2}\right)\right) + \frac{4 \cos\left(v\right)}{2 - \sin\left(v\right)^{2} \cos\left(u\right)^{2}}

Properties

Family
constant-curvature
Given by
a parametrisation
Curvature
constant positive Gaussian curvature
Periodicity
not periodic
Ends
0
Embedding
self-intersecting
Fidelity
exact
Exactness
elementary

Sources

Chart as curated in tools/surfdb/charts.py, verified numerically against the curvature condition the record claims (measured over the chart by the validator and the charts self-test).