# Dini's surface

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

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]

$x=a\cos\left(u\right)\sin\left(v\right)$
$y=a\sin\left(u\right)\sin\left(v\right)$
$z=a\left(\cos\left(v\right)+\ln\left(\tan\left(\frac{v}{2}\right)\right)\right)+bu$

Another description is a helicoid constructed from the tractrix.[4]

## Uses

Renditions of Dini's surface have appeared on the covers of Western Kentucky University's Graduate Study in Mathematics, Gray's Modern Differential Geometry of Curves and Surfaces with Mathematica, Second Edition, and volume 2, number 3 of La Gaceta de la Real Sociedad Matemática Española.

2. ^ J J O'Connor and E F Robertson (2000). "Ulisse Dini Biography". School of Mathematics and Statistics, University of St Andrews, Scotland. Retrieved 209-11-14. Check date values in: |accessdate= (help)