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Bohemian Dome

\begin{figure}\begin{center}\BoxedEPSF{BohemianDome.epsf scaled 600}\end{center}\end{figure}

A Quartic Surface which can be constructed as follows. Given a Circle $C$ and Plane $E$ Perpendicular to the Plane of $C$, move a second Circle $K$ of the same Radius as $C$ through space so that its Center always lies on $C$ and it remains Parallel to $E$. Then $K$ sweeps out the Bohemian dome. It can be given by the parametric equations

$\displaystyle x$ $\textstyle =$ $\displaystyle a\cos u$  
$\displaystyle y$ $\textstyle =$ $\displaystyle b\cos v+a\sin u$  
$\displaystyle z$ $\textstyle =$ $\displaystyle c\sin v$  

where $u,v\in [0,2\pi)$. In the above plot, $a=0.5$, $b=1.5$, and $c=1$.

See also Quartic Surface


Fischer, G. (Ed.). Mathematical Models from the Collections of Universities and Museums. Braunschweig, Germany: Vieweg, pp. 19-20, 1986.

Fischer, G. (Ed.). Plate 50 in Mathematische Modelle/Mathematical Models, Bildband/Photograph Volume. Braunschweig, Germany: Vieweg, p. 50, 1986.

Nordstrand, T. ``Bohemian Dome.''

© 1996-9 Eric W. Weisstein