Bohemian Dome

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

$$x = a\cos u$$

$$y = b\cos v+a\sin u$$

$$z = c\sin v$$

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

See also Quartic Surface

References

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.'' http://www.uib.no/people/nfytn/bodtxt.htm.