MATHS BITE: Dini’s Surface

Dini’s surface, named after Ulisse Dini, is a surface with constant negative curvature that can be created by twisting a pseudosphere (see picture below).

Pseudosphere

Dini’s surface is given by the following parametric equations:

{\displaystyle {\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}}}

 

 

Dini’s Surface

Dini’s surface is pictured in the upper right-hand corner of a book by Alfred Gray (1997), as well as on the cover of volume 2, number 3 of La Gaceta de la Real Sociedad Matem├ítica Espa├▒ola (1999).

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