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The funnel surface is a Regular Surface defined by the Cartesian equation

z={\textstyle{1\over 2}}\ln(x^2+y^2)
\end{displaymath} (1)

and the parametric equations
$\displaystyle x(r,\theta)$ $\textstyle =$ $\displaystyle r\cos\theta$ (2)
$\displaystyle y(r,\theta)$ $\textstyle =$ $\displaystyle r\sin\theta$ (3)
$\displaystyle z(r,\theta)$ $\textstyle =$ $\displaystyle \ln r.$ (4)

See also Gabriel's Horn, Pseudosphere, Sinclair's Soap Film Problem


Gray, A. Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, pp. 325-327, 1993.

© 1996-9 Eric W. Weisstein