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Dini's Surface


A surface of constant Negative Curvature obtained by twisting a Pseudosphere and given by the parametric equations

$\displaystyle x$ $\textstyle =$ $\displaystyle a\cos u\sin v$ (1)
$\displaystyle y$ $\textstyle =$ $\displaystyle a\sin u\sin v$ (2)
$\displaystyle z$ $\textstyle =$ $\displaystyle a\{\cos v+\ln[\tan({\textstyle{1\over 2}}v)]\}+bu.$ (3)

The above figure corresponds to $a=1$, $b=0.2$, $u\in [0, 4\pi]$, and $v\in (0, 2]$.

See also Pseudosphere


Geometry Center. ``Dini's Surface.''

Gray, A. Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, pp. 494-495, 1993.

Nordstrand, T. ``Dini's Surface.''

© 1996-9 Eric W. Weisstein