A Surface which can be swept out by a moving Line in space and therefore has a parameterization
of the form

(1) |

Examples of ruled surfaces include the elliptic Hyperboloid of one sheet (a doubly ruled surface)

(2) |

(3) |

(4) |

(5) |

The only ruled Minimal Surfaces are the Plane and Helicoid (Catalan 1842, do Carmo 1986).

**References**

Catalan E. ``Sur les surfaces réglées dont l'aire est un minimum.'' *J. Math. Pure. Appl.* **7**,
203-211, 1842.

do Carmo, M. P. ``The Helicoid.'' §3.5B in
*Mathematical Models from the Collections of Universities and Museums* (Ed. G. Fischer).
Braunschweig, Germany: Vieweg, pp. 44-45, 1986.

Fischer, G. (Ed.). Plates 32-33 in
*Mathematische Modelle/Mathematical Models, Bildband/Photograph Volume.*
Braunschweig, Germany: Vieweg, pp. 32-33, 1986.

Gray, A. ``Ruled Surfaces.'' Ch. 17 in
*Modern Differential Geometry of Curves and Surfaces.*
Boca Raton, FL: CRC Press, pp. 333-355, 1993.

© 1996-9

1999-05-25