Page "Curvature" Paragraph 24

The signed curvature depends on the particular parametrization chosen for a curve.

For example the unit circle can be parametrised by ( counterclockwise, with k > 0 ), or by ( clockwise, with k < 0 ).

More precisely, the signed curvature depends only on the choice of orientation of an immersed curve.

Every immersed curve in the plane admits two possible orientations.