Dini Surface (mathmum)

A B Cron
In geometry, Dini's surface is a surface with constant negative curvature that can be created by twisting a pseudosphere. It is named after Ulisse Dini and described by the following parametric equations: x=a cos(u) sin(v) y=a sin(u) sin(v) z=a (cos(v) + ln(tan(v/2)))+b u Surface[ <Expression>, <Expression>, <Expression>, <Parameter Variable 1>, <Start Value>, <End Value>, <Parameter Variable 2>, <Start Value>, <End Value> ] c = Surface[((a * cos(u)) * sin(v)), ((a * sin(u)) * sin(v)), (a * (cos(v) + log(tan((0.5 * v))))) + (b * u), u, 0, 12.566370614359172, v, 0.01, 2]
Your examples recall me a Dini's surface. It's a classical example of a surface having constant negative curvature, well described by an Italian mathematician, Ulisse Dini. Play with a, b in the following worksheet. For further information: http://mathworld.wolfram.com/DinisSurface.html https://en.wikipedia.org/wiki/Dini's_surface mathmum file