# Catalan surface

From Encyclopedia of Mathematics

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 $r=\rho(u)+vl(u)$, 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.

#### References

- [1] 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) Zbl 0366.53001
- [a2] R.S. Millman, G.D. Parker, "Elements of differential geometry" , Prentice-Hall (1977) pp. 31–35 Zbl 0425.53001

**How to Cite This Entry:**

Catalan surface.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Catalan_surface&oldid=52741

This article was adapted from an original article by I.Kh. Sabitov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article