Dini's surface

In geometry, Dini's surface is a surface with constant negative curvature that can be created by twisting a pseudosphere.

[1] It is named after Ulisse Dini[2] and described by the following parametric equations:[3] Another description is a generalized helicoid constructed from the tractrix.

[4]

Dini's surface plotted with adjustable parameters by Wolfram Mathematica program
Dini's Surface with constants a = 1, b = 0.5 and 0 ≤ u ≤ 4 π and 0<v<1.
Dini's surface with 0 ≤ u ≤ 4 π and 0.01 ≤ v ≤ 1 and constants a = 1.0 and b = 0.2.