What kind of path does a Klingon vessel being pulled by a tractor beam from the Enterprise moving along a line (the x-axis in this graph)? The tractor beam has a fixed length that you enter and points toward where the Klingon vessel started on the y-axis.
The path of the Klingon vessel is an example of a locus. This particular locus is calle a tractrix. In the three dimensional version of this problem the tractrix is spun around the x-axis. The surface formed can be used to model a non-Euclidean Geometry. What changes in the path occur when the length of the tractor beam changes?