While teaching a course in differential geometry, I came up with the following problem, which I think is cool.

Assume $\gamma$ is a closed geodesic on a sphere $\Sigma$ with positive Gauss curvature.
Can it look like one of the following curves in a parametrization of $\Sigma\backslash\{\text{point}\}$ by the plane?

[![enter image description here][1]][1]

>I expect that there is a theorem that answers all questions like this. Is it indeed so?


  [1]: https://i.sstatic.net/GUQYT.png