A ruled surface whose rectilinear generators are all parallel to the same plane. Its line of restriction (cf. Ruled surface) is planar. The position vector of a Catalan surface is , where , . If all the generators of a Catalan surface intersect the same straight line, then the surface is a conoid.
|||E. Catalan, "Mémoire sur les surfaces gauches à plan directeur" , Paris (1843)|
|[a1]||W. Klingenberg, "A course in differential geometry" , Springer (1978) (Translated from German)|
|[a2]||R.S. Millman, G.D. Parker, "Elements of differential geometry" , Prentice-Hall (1977) pp. 31–35|
Catalan surface. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Catalan_surface&oldid=18468