The Pseudosphere and Tractrix

This demo shows a tractrix, and its surface of revolution, the pseudosphere. Moving the hotspot in the 'Pseudosphere' window draws the slice curve in the vertical place through the origin and the hotspot. The 'Slice' window shows the tangent and normal vectors and the osculating circle of the tractrix at the hotspot.

The white line segment which meets the y-axis in the 'Slice' window is the subnormal. It's length is the radius of the white sphere in the 'Pseudosphere' window which meets the pseudosphere along a parallel of latitude at the hotspot.