Seiffert's spiral

Seiffert's spherical spiral is a curve on a sphere made by moving on the sphere with constant speed and angular velocity with respect to a fixed diameter. (If one takes the diameter to be the line from the north pole to the south pole, then the requirement of constant angular velocity means that the longitude of the moving point is changing at a constant rate.) The cylindrical coordinates of the varying point on this curve turn out to be given by the Jacobian elliptic functions.