Dini's surface

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]

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

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

References

^ "Wolfram Mathworld: Dini's Surface". Retrieved 2009-11-12.
^ J J O'Connor and E F Robertson (2000). "Ulisse Dini Biography". School of Mathematics and Statistics, University of St Andrews, Scotland. Archived from the original on 2012-06-09. Retrieved 2016-04-12.
^ "Knol: Dini's Surface (geometry)". Archived from the original on 2011-07-23. Retrieved 2009-11-12.
^ Rogers and Schief (2002). Bäcklund and Darboux transformations: geometry and modern applications in Soliton Theory. Cambridge University Press. pp. 35–36.