Dini's surface

File:Mathematica dinis surface.png

Dini's surface plotted with adjustable parameters by Wolfram Mathematica program

File:Dini Surface.png

Dini's Surface with constants a = 1, b = 0.5 and 0 ≤ u ≤ 4Template:Pi and 0<v<1.

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:

$\begin{array}{rl}x& =a\cos u\sin v\\ y& =a\sin u\sin v\\ z& =a(\cos v+\ln \tan \frac{v}{2})+bu\end{array}$

File:Dini's Surface.svg

Dini's surface with 0 ≤ u ≤ 4Template:Pi and 0.01 ≤ v ≤ 1 and constants a = 1.0 and b = 0.2.

Another description is a generalized helicoid constructed from the tractrix.

See also

• Breather surface
• Kuen surface