The [color=#ff0000][i]Dini's surface[/i][/color] shown in the applet is a particular [color=#0000ff][i]surface having constant negative curvature[/i][/color], described by the Italian mathematician [url=https://en.wikipedia.org/wiki/Ulisse_Dini][u]Ulisse Dini[/u][/url].[br][br]The surface parametric equations are:[br][math]x=a \cdot cos(u) sin(v)[/math] [br][math]x=a \cdot sin(u) sin(v)[/math] [br][math]x=a \left( cos(v) + ln \left( tan \left( \frac{1}{2}v \right) \right ) \right )+b \; u[/math] [br][br]Move sliders [i]a[/i], [i]b [/i] to explore how these values affect the [i]Dini's surface[/i], shown in the applet for [math]u \in [0,4\pi], \; v \in (0,2] [/math].