View source for Catalan surface

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A [[Ruled surface|ruled surface]] whose rectilinear generators are all parallel to the same plane. Its line of restriction (cf. [[Ruled surface|Ruled surface]]) is planar. The position vector of a Catalan surface is $r=\rho(u)+vl(u)$, where $l''(u)\neq0$, $(l,l',l'')=0$. If all the generators of a Catalan surface intersect the same straight line, then the surface is a [[Conoid|conoid]].

====References====

* {{Ref|1}} E. Catalan, "Mémoire sur les surfaces gauches à plan directeur" , Paris  (1843)
* {{Ref|a1}} W. Klingenberg, "A course in differential geometry" , Springer  (1978)  (Translated from German) {{ZBL|0366.53001}}
* {{Ref|a2}} R.S. Millman, G.D. Parker,   "Elements of differential geometry" , Prentice-Hall  (1977)  pp. 31–35 {{ZBL|0425.53001}}