In geometry, [b]Dini's surface[/b] is a surface with constant negative [b]curvature[/b] that can be created by twisting a [b]pseudosphere[/b]. It is named after [b]Ulisse Dini[/b] and described by the following [b]parametric equations[/b]: 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: [url]http://mathworld.wolfram.com/DinisSurface.html[/url] [url]https://en.wikipedia.org/wiki/Dini's_surface[/url] [url=http://forum.geogebra.org/viewtopic.php?f=52&t=41165&sid=9b09dee30fdb5a07c190e2a0c16d5c94]mathmum file[/url]