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CATALAN SURFACE

Eugene Charles Catalan (1814-1894): Franco-Belgian mathematician.
Other name: ruled surface with directrix plane. |

Cartesian parametrization: ,
reunion of the lines D
passing through
and directed by
with ._{u} |

A Catalan surface is a ruled
surface the generatrices of which remain parallel to a fixed plane,
called the *directrix plane*, in other words, a ruled surface the
directrix cone of which is planar.

Examples: the cylinders, the conoids, the ruled helicoids with directrix plane.

Do not mistake these for Catalan's
minimal surface.

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© Robert FERRÉOL 2017