A curve in three-space is said to have self-linking number n if the curve has linking number n with the push-off curve in the direction of the principal normal vector. The notion was first described by Calugareanu [C1] and rediscovered and extended by Pohl

To see a curve on the three-sphere rotating in red and white, activate the movie

To see a curve on the three-sphere rotating with nice colors but low resolution, activate the movie

A much nicer movie shows the curve and its pushoffs as a series of colored bands.

Another movie shows the curve "pass through infinity" in three-space by passing through the center of projection in four-space.

[Right] Self-Linking for Curves in Three-Space
[Right] Letter to Kuiper on Torus Knots on the Three-Sphere