Summary

Development of the unit circle in three-dimensional Euclidean space, with the affine connection preserving the Euclidean structure having torsion proportional to the cross product. The four connections have the form ${\displaystyle \nabla _{e_{i}}e_{j}=\tau e_{i}\times e_{j}}$, with ${\displaystyle \tau =0.01,0.1,0.5,1.0}$. All four curves have curvature 1, and the respective curve has torsion (as a curve in the Euclidean space) ${\displaystyle \tau }$. The file has been generated in sagemath, and cropped in Gimp.

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