Conoid
From Encyclopedia of Mathematics
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A Catalan surface all straight line generators of which intersect a fixed straight line, called an axis of the conoid. For example, a hyperbolic paraboloid is a conoid with two axes.
The position vector of a conoid is given by
 |
where 
is a unit vector having the same direction as an axis of the conoid and 
is some function. For a right conoid 
, 
, and then its axis is a line of striction. A right conoid with 
is a helicoid.
Comments
References
| [a1] | M. Berger, B. Gostiaux, "Géométrie différentielle: variétés, courbes et surfaces" , Presses Univ. France (1987) |
| [a2] | M.P. Do Carmo, "Differential geometry of curves and surfaces" , Prentice-Hall (1976) |
How to Cite This Entry:
Conoid. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Conoid&oldid=18035
Conoid. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Conoid&oldid=18035
This article was adapted from an original article by I.Kh. Sabitov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article